Recent Developments in String Phenomenology

Gary Shiu University of Wisconsin-Madison String Phenomenology

• The last time I gave a plenary talk at Pheno was in 2002, the year when the ﬁrst String Pheno Conference was held (in Oxford).

• The annual Pheno and Strings conferences both started in the 80s. String Phenomenology

• The last time I gave a plenary talk at Pheno was in 2002, the year when the ﬁrst String Pheno Conference was held (in Oxford).

• The annual Pheno and Strings conferences both started in the 80s.

Pheno String

String Pheno String Pheno Turns 18! String Phenomenology 2019 (24-28 June 2019) · Indico 5/1/19, 11'15 AM

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String Phenomenology 2019

24-28 June 2019 CERN Europe/Zurich timezone

Overview This conference is part of the String Geometry and String Phenomenology Institute (17-28 June). Timetable The annual String Phenomenology conference discusses recent progress in compactiﬁcations of Registration string theory and their relation to particle physics and cosmology. Green Tips

Poster

Previous Conferences Topics include:

Computer Access Swampland and Quantum Gravity Conjectures

Health insurance, VISA Formal and Mathematical Aspects of string compactifications (such as F-theory, G2 compactifications, heterotic compactifications, and other corners of the string landscape, e.g. Accommodation non-geometric compactifications) Directions to and inside String Model Building in particle physics and cosmology CERN Machine Learning Techniques to explore the String Landscape Funding

https://indico.cern.ch/event/782251/ Page 1 of 3 Strings Meet Phenomenology

• After the discovery of anomaly cancellation [Green, Schwarz, ’84], it was soon realized that string theory provides a consistent framework for unifying particle physics with gravity.

• This is followed by the heterotic string [Gross, Harvey, Martinec, Rohm,’85] and Calabi-Yau compactiﬁcation [Candelas, Horowitz, Strominger, Witten, ’85].

• To make contact with phenomenology:

4d M6d x

• Physical properties of our universe (# of families, particle’s quantum numbers and couplings, etc) are encoded by the size and shape of the extra dimensions. String Theory Landscape

F-theory M-theory Type IIB Type IIA

Heterotic Type I String Theory Landscape

F-theory M-theory Type IIB Type IIA

Heterotic Type I String Theory Landscape

10500 “vacua” [Douglas ’03] F-theory M-theory Type IIB Type IIA

Heterotic Type I String Theory Landscape

10272,000 “vacua” 10500 “vacua” [Taylor, Wang, ’15] [Douglas ’03] F-theory M-theory Type IIB Type IIA

Heterotic Type I String Landscape and Phenomenology

• String theory seems to admit a vast number of 4d solutions

• They represent an enormously rich landscape of EFTs

• Field theoretical ideas in particle physics and cosmology have found their UV realizations in string theory.

• New scenarios have been uncovered along the way.

• This traditional approach leaves the impression that every consistent-looking EFT can be embedded in string theory

Are there low energy effective theories that are not embeddable in string theory? Landscape vs Swampland

Landscape Landscape vs Swampland

Swampland [Vafa, ’05] Landscape Landscape vs Swampland

Swampland [Vafa, ’05] Landscape

What properties delineate the landscape from the swampland? What are the phenomenological consequences? Swampland Conjectures

We don’t have yet theorems that fully delineate the landscape from the swampland, but ∃ an intricate web of well-tested conjectures:

Weak Gravity Conjecture Distance Conjecture [Arkani-Hamed, Motl, Nicolis, Vafa. ’06] [Ooguri, Vafa. ’06]

dS Conjecture [Obied, Ooguri, Spodyneiko, Vafa,’18]; [Ooguri, Palti, GS, Vafa, ’18]

These conjectures were developed based on general properties of quantum gravity (e.g., black holes) and string constructions. Quantum Gravity and Global Symmetries Quantum Gravity and Global Symmetries

• Global symmetries are expected to be violated by gravity:

Q, M

Q, Mp

• No hair theorem: Hawking radiation is insensitive to Q.

➡ Inﬁnite number of states (remnants) with m . Mp ➡ Violation of entropy bounds. At ﬁnite temperature (e.g. in Rindler space), the density of states blows up. Susskind ‘95

• Swampland conjecture: theories with exact global symmetries are not UV-completable.

• In (perturbative) string theory, all symmetries are gauged

• Many phenomenological ramiﬁcations, e.g., mini-charged DM comes with a new massless gauge boson [GS, Soler, Ye, ’13]. The Weak Gravity Conjecture

Arkani-Hamed, Motl, Nicolis, Vafa ‘06 The Weak Gravity Conjecture

Arkani-Hamed, Motl, Nicolis, Vafa ‘06 • The conjecture:

“Gravity is the Weakest Force”

• This is a scale-dependent statement, but as we’ll see, the WGC comes with a UV cutoff Λ (magnetic WGC).

• For every long range gauge ﬁeld there exists a particle of charge q and mass m, s.t. q M “1” m P • Applying the WGC to magnetically charged states imply:

2 qmag ∼ 1/g, mmag ∼ Λ/g ⇒ Λ ≲ g(Λ)MP The Weak Gravity Conjecture

Arkani-Hamed, Motl, Nicolis, Vafa ‘06 • The conjecture:

“Gravity is the Weakest Force”

• This is a scale-dependent statement, but as we’ll see, the WGC comes with a UV cutoff Λ (magnetic WGC).

• For every long range gauge ﬁeld there exists a particle of charge q and mass m, s.t.

q QExt MP “1” MP m ⌘ MExt • Applying the WGC to magnetically charged states imply:

2 qmag ∼ 1/g, mmag ∼ Λ/g ⇒ Λ ≲ g(Λ)MP The Weak Gravity Conjecture

• Take U(1) gauge theory and a scalar with m>qMp F F F F e + g g + e

•1Stable Introduction bound states: the original argument EBH .... we did some really awesome things in the... past and here is another... awesome paper... 2m>M2 > 2q 3m>M3 > 3q Nm > MN >Nq M Q 1 ! 1 2 Remnants Revisited • All these BH states are exactly stable. In particular, large bound states The(charged Weak Gravity black Conjecture holes) do was not originally Hawking motivated radiate by once a desire they to reach avoid ‘remnants’.the In theextremal words of [1]: limit M=Q, equiv. T=0.

“...there should not exist a large number of exactly stable objects (extremal black holes) whose stability is not protected by any symmetries.”

Arkani-Hamed et al. ‘06 The proposed conjecture in [1] was thus designed to eliminate the inﬁnite tower of extremal black holes from the spectrum of stable objects. However, string theory itself contains alarge,infact,inﬁnite, number of exactly stable black holes and so it is not immediately clear why these should be acceptable while, presumably, some other class of remnants is not. To understand this issue better, let us review the arguments against remnants presented in [2]. Consider the spontaneous production of states in Rindler space:

ds2 = ⇢2dt2 + d⇢2 + dx2 (2.1) ? 1 An object of mass M centered at ⇢ feels an e↵ective temperature of T =(2⇡⇢) . If there are eS ‘species’ of this object then standard thermodynamics tells us that the equilibrium density is: 2⇡⇢M+S N e (2.2) ⇠ Under the ‘remnant hypothesis’, black holes of arbitrary initial mass decay to Planck scale remnants where the entropy of the initial configuration is stored. In this case, the number of ‘species’ eS must clearly be infinite and the remnant density diverges at any ⇢.On the other hand, Rindler space is simply a coordinate transform of Minkowski space, which has zero vacuum energy density. Thus, such theory does not transform sensibly under di↵eomorphisms and is not a good candidate for describing quantum gravity. The salient feature of this argument is that it eliminates remnants, even while accom- modating an infinite tower of black holes. To see how, note that the number of ‘species’

SBH associated with a 4d Schwarzschild black is given by e , where SBH is the Beckenstein- Hawking entropy, A/4G. Thus, the density is:

2⇡⇢M+4⇡GM 2 N = e (2.3)

1 The Weak Gravity Conjecture

• Take U(1) gauge theory and a scalar with m>qMp F F F F e + g g + e

“...there should not exist a large number of exactly stable objects (extremal black holes) whose stability is not protected by any symmetries.” ? Arkani-Hamed et al. ‘06 The proposed conjecture in [1] was thus designed to eliminate the inﬁnite tower of extremal black holes from the spectrum of stable objects. However, string theory itself contains alarge,infact,inﬁnite, number of exactly stable black holes and so it is not immediately clear why these should be acceptable while, presumably, some other class of remnants is not. To understand this issue better, let us review the arguments against remnants presented in [2]. Consider the spontaneous production of states in Rindler space:

SBH associated with a 4d Schwarzschild black is given by e , where SBH is the Beckenstein- Hawking entropy, A/4G. Thus, the density is:

2⇡⇢M+4⇡GM 2 N = e (2.3)

1 The Weak Gravity Conjecture

• Take U(1) gauge theory and a scalar with m>qMp F F F F e + g g + e

• Stable bound states: the original argument ...... EBH 2m>M2 > 2q 3m>M3 > 3q Nm > MN >Nq M Q 1 ! 1

• All these BH states are exactly stable. In particular, large bound states (charged black holes) do not Hawking radiate once they reach the extremal limit M=Q, equiv. T=0.

• In order to avoid a large number of exactly stable states one must demand the existence of some particle with q Q 1 ext = m Mext Mp Evidences for the WGC Evidences for the Weak Gravity Conjecture

Several lines of argument have been taken (so far):

• Holography [Nakayama, Nomura, ’15];[Harlow, ‘15];[Benjamin, Dyer, Fitzpatrick, Kachru, ‘16];[Montero, GS, Soler, ’16] • Cosmic Censorship [Horowitz, Santos, Way, ’16];[Crisford, Horowitz, Santos, ’17] • Black hole thermodynamics [Cottrell, GS, Soler, ’16] [Fisher, Mogni, ’17]; [Cheung, Liu, Remmen, ’18];[Hamada, Noumi, GS, ’18]

• IR Consistencies (unitarity & causality) [Cheung, Remmen, ’14] [Andriolo, Junghans, Noumi, GS,’18];[Hamada, Noumi, GS, ’18] Evidences for stronger versions of the WGC:

• Consistencies with T-duality [Brown, Cottrell, GS, Soler, ‘15] and dimensional reduction [Heidenreich, Reece, Rudelius ’15]. • Modular invariance + charge quantization suggest a sub-lattice WGC [Montero, GS, Soler, ‘16] (see also [Heidenreich, Reece, Rudelius ’16]). WGC and Inﬂation Primordial Gravitational Waves

Planck Collaboration: Constraints on inﬂation 55

PLANCK 2015 7 1 BK+P 1 B+P 6 ]

K+P 2

0.8 0.8 K µ 5 Joint 0.6 BICEP-Planck 0.6 4 peak peak

L/L L/L 3 0.4 0.4 2 @ l=80 & 353 GHz [ d

0.2 0.2 A 1

0 0 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 1 2 3 4 5 6 7 0 0.05 0.1 0.15 0.2 0.25 0.3 A @ l=80 & 353 GHz [ K2] r d µ r

Fig. 54. Marginalized joint 68 % and 95 % CL regions for ns and r0.002 from Planck alone and in combination with its cross- correlationMany with BICEP2/Keck experiments Array and/or BAO data compared including with the theoretical predictions BICEP/KECK, of selected inflationary models. PLANCK, ACT, further improving on the upper limits obtained from the different Table 17. Results of inflationary model comparison using the data combinationsPolarBeaR, presented in Sect. 5. SPT, SPIDER,cross-correlation QUEIT, between BICEP2/Keck Clover, Array and Planck EBEX,. This QUaD, … By directly constraining the tensor mode, the BKP likeli- table is the analogue to Table 6, which did not use the BKP like- hood removes degeneracies between the tensor-to-scalar ratio lihood. -2 and othercan parameters. potentially Adding tensors and running, detect we obtain primordial B-mode at the sensitivity r~10 . Inflationary Model ln B0X r0.002 < 0.10 (95 % CL, Planck TT+lowP+BKP) , (168) wint = 0 wint , 0 whichFurther constitutes almost experiments, a 50 % improvement over the Plancksuch as CMB-S4,R + R2/6M2 ...PIXIE,+0.3 LiteBIRD, DECIGO, TT+lowP constraint quoted in Eq. (28). These limits on tensor n = 2 6.0 5.6 Natural 5.6 5.0 modes are more robust than the limits using the shape of the -3 CAli,TT spectrum .. alone may owing toimprove the fact that scalar perturbations further theHilltop sensitivity (p = 2) 0.7 to0.4 eventually reach r ~ 10 . ` Hilltop (p = 4) 0.6 0.9 cannot generate B modes irrespective of the shape of the scalar Double well 4.3 4.2 spectrum. Brane inflation (p = 2) +0.20 .0 Brane inflation (p = 4) +0.1 0.1 . . 13.1. Implications of BKP on selected inflationary models Exponential inflation 0 100 SB SUSY 1.8 1.5 Using the BKP likelihood further strengthens the constraints Supersymmetric ↵-model 1.1 +0.1 Superconformal (m = 1) 1.9 1.4 on the inflationary parameters and models discussed in Sect. 6, as seen in Fig. 54. If we set ✏3 = 0, the first slow-roll pa- rameter is constrained to ✏1 < 0.0055 at 95 % CL by Planck TT+lowP+BKP. With the same data combination, concave po- BKP reduces the Bayes factor of the hilltop models compared 2 tentials are preferred over convex potentials with log B = 3.8, to R , because these models can predict a value of the tensor-to- which improves on log B = 2 obtained from the Planck data scalar ratio that better fits the statistically insignificant peak at r 0.05. See Table 17 for the Bayes factors of other inflationary alone. ⇡ Combining with the BKP likelihood strengthens the con- models with the same two cases of post-inflationary evolution straints on the selected inflationary models studied in Sect. 6. studied in Sect. 6. Using the same methodology as in Sect. 6 and adding the BKP 2 likelihood gives a Bayes factor preferring R over chaotic in- 13.2. Implications of BKP on scalar power spectrum flation with monomial quadratic potential and natural inflation by odds of 403:1 and 270:1, respectively, under the assumption The presence of tensors would, at least to some degree, require of a dust equation of state during the entropy generation stage. an enhanced suppression of the scalar power spectrum on large TT The combination with the BKP likelihood further penalizes the scales to account for the low-` deficit in the C` spectrum. We double-well model compared to R2 inflation. However, adding therefore repeat the analysis of an exponential cut-off studied B-mode and UV Sensitivity

A detection at the targeted level implies that the inflaton potential is nearly flat over a super-Planckian field range: r 1/2 M Lyth ’96 & 0.01 Pl ⇣ ⌘

“Large ﬁeld inﬂation” are highly sensitive to UV physics Axions and ALPs

The QCD axion [Wilczek, ’78]; [Weinberg, ’78] was introduced in the context of the Pecci-Quinn mechanism and the strong CP problem.

An axion enjoys a perturbative shift symmetry.

String theory has many higher-dimensional form-ﬁelds:

e.g.

3-form ﬂux 2-form gauge potential:

gauge symmetry:

Integrating the 2-form over a 2-cycle gives an axion-like particle (ALP):

The gauge symmetry becomes a shift symmetry, that is broken by non-perturbative (instanton) eﬀects. WGC and Axions

• Consider a U(1) gauge theory in 5d, and compactify on S to 4d. Upon dimensional reduction: A (x, x ) (A (x), (x)) M 4 ! µ 1 1 1 S = d5x F F MN d4x F F µ⌫ @ @µ 4g2 MN ! 4g2 µ⌫ 2 µ Z 5 Z ✓ 4 ◆ • The gauge symmetry leads to an axion shift symmetry = + c

• Topologically non-trivial Euclidean conﬁgurations (instantons) with charged ﬁelds wrapping the 5d circle generate a potential

Sinst =2⇡Rm5 Sinst V ()=e cos p f f = q5 2⇡R ✓ ◆

• 3 The 5d WGC for charged particles m 5

f Sinst Mp More generally, using duality: ·  Brown, Cottrell, GS, Soler, ‘15 Axions & Large Field Inﬂation

Natural Inflation [Freese, Frieman, Olinto] Pseudo-Nambu-Goldstone bosons are natural inflaton candidates. Axions & Large Field Inflation

Natural Inflation [Freese, Frieman, Olinto] Pseudo-Nambu-Goldstone bosons are natural inflaton candidates. They satisfy a shift symmetry that is only broken by non-perturbative effects:

decay constant Axions & Large Field Inﬂation

Natural Inflation [Freese, Frieman, Olinto] Pseudo-Nambu-Goldstone bosons are natural inflaton candidates. They satisfy a shift symmetry that is only broken by non-perturbative effects:

Slow roll: f>MP decay constant

(n+1) (1) (k) k ⇤ S V ()=1 ⇤ cos + ⇤ 1 cos if e inst << 1 f f ⇤(n) ⇠ ✓ ◆ k>X1  ✓ ◆ Axions & Large Field Inﬂation

Natural Inflation [Freese, Frieman, Olinto] Pseudo-Nambu-Goldstone bosons are natural inflaton candidates. They satisfy a shift symmetry that is only broken by non-perturbative effects:

Slow roll: f>MP decay constant

(n+1) (1) (k) k ⇤ S V ()=1 ⇤ cos + ⇤ 1 cos if e inst << 1 f f ⇤(n) ⇠ ✓ ◆ k>X1  ✓ ◆ The WGC implies that these conditions cannot be simultaneously satisﬁed. WGC and Axion Inﬂation

• Models with multiple axions (N-ﬂation, KNP-alignment,…) have been proposed to obtain large ﬁeld ranges

• The WGC in all direction in charge space (i.e. requiring all extremal black holes to be unstable) constrains these models

Brown, Cottrell, GS, Soler, ’15… • ∃ Loopholes (e.g., spectator instantons).

• Axion monodromy is an interesting exception. [Silverstein, Westphal];[McAllister, Silverstein, Westphal]; [Marchesano, GS, Uranga]

It is however subject to other swampland constraints (e.g., distance conjecture) though models with ∆ϕ ~ 5-10 MP seems compatible with quantum gravity [Landete, GS, ’18] WGC and Fuzzy Dark Matter WGC and Fuzzy DM

• The standard ΛCDM model is highly successful on scales >10kpc.

• At smaller distances, discrepancies arise between observations and structure formation predicted by simulations [Weinberg et al, ’13]

• An ultralight scalar may alleviate some of these problems:

22 21 10 eV . m . 10 eV

• Its large Compton wavelength suppresses structure formation at small scales

• Natural to think of ultralight axions as FDM candidates [Hu, Barkana, Gruzinov, ’00]; recent revival of interest [Hui, Ostriker, Tremaine, Witten, ‘16] WGC and Fuzzy DM

• For axionic FDM, the decay constant f can be estimated through relic density (obtained by misalignment mechanism):

2 1/2 2 f m 2 ⌦DM h 0.1 17 22 ✓i f(✓i) ⇡ 10 GeV 10 eV h i ✓ ◆ ⇣ ⌘

• DM density: ⌦ h2 0.1 DM ⇡

• ✓ i Initial misalignment.

• Anharmonicity of potential: f(✓i) 0 ✓i ⇡ • For ✓ 1 , FDM corresponds to: i ⇡

22 21 17 16 • 10 eV m 10 eV 10 GeV f 5 10 GeV . . ! & & ⇥ WGC and Fuzzy DM

• Consider an instanton-induced axion mass

2 2 S 2 2 S V ()=⇤ f e inst 1 cos = m = ⇤ e inst f )  ✓ ◆ • Take ﬁrst Λ=Mp (c.f. gravitational instantons/wormholes):

21 16 m<10 GeV f 5 10 GeV ⇥ = = f Si & 5MP 2 ) 8 ) · ⌦DM h 0.1 < Si 222 ⇡ in tension with WGC • Way out I: Λ << Mp : Hebecker, Mikhail, Soler, ’18

12 f S = M = ⇤ 10 eV · inst p ) . • Way out II: ✓i ⇡ f(✓i) WGC ⇒ θ ≳ 0.91π ! !1 i • Way out III: loopholes to WGC (spectator instantons) Is Λ > 0 in the Swampland? Λ > 0 vacua in String Theory

• Observation of accelerating universe poses the dark energy puzzle. The prevailing view is that we are living in a metastable dS vacuum (though it remains to be seen experimentally, [Dodelson’s talk]).

• Notoriously difficult to construct controlled dS string vacua. Part of the difficulty can be traced to the Dine-Seiberg problem: • In string theory, there are no free parametersgs = e : coupling constants are vevs of scalar fields (moduli):

• At zero coupling (ϕ→∞), the vacuum energy always vanishes V () No vacua (regardless of the cc) unless there is a competition V () ae + ... ⇠ between terms of different orders

Λ > 0 vacua in String Theory

• Observation of accelerating universe poses the dark energy puzzle. The prevailing view is that we are living in a metastable dS vacuum.

• Notoriously difﬁcult to construct controlled dS string vacua. Part of the difﬁculty can be traced to the Dine-Seiberg problem:

• In string theory, there are no free parameters: coupling constants are vevs of scalar ﬁelds (moduli): gs = e

• At zero coupling (ϕ→∞), the vacuum energy always vanishes V ()

Competition between 2 terms of V(ϕ) = ae−ϕ − be−2ϕ + … different orders only gives AdS vacua Λ > 0 vacua in String Theory

• Observation of accelerating universe poses the dark energy puzzle. The prevailing view is that we are living in a metastable dS vacuum.

• Notoriously difﬁcult to construct controlled dS string vacua. Part of the difﬁculty can be traced to the Dine-Seiberg problem:

• In string theory, there are no free parameters: coupling constants are vevs of scalar ﬁelds (moduli): gs = e

• At zero coupling (ϕ→∞), the vacuum energy always vanishes V () dS vacua require at least 3 terms of different orders to compete V(ϕ) = ae−ϕ − be−2ϕ + ce−3ϕ + … CALT-TH 2018-042, IPMU 18-0164, MPP-2018-248, MAD-TH-18-06

Distance and de Sitter Conjectures on the Swampland

1, 2 3 PACS numbers:4 04.60.-m, 11.25.-w 5 Distance and de Sitter ConjecturesHirosi Ooguri, on theEran Swampland Palti, Gary Shiu, and Cumrun Vafa 1Walter Burke Institute for Theoretical Physics, Caltech, Pasadena, CA 91125, USA 2Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa 277-8583, Japan 1, 2 3 4 5 INTRODUCTION sistent quantum gravity must satisfy either, Hirosi Ooguri, 3Max-Planck-InstitutEran Palti, Gary für Shiu, Physik (Werner-Heisenberg-Insand Cumrun Vafa titut), Fohringer Ring 6, 80805 Munchen, Germany 1 4Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA c Walter Burke Institute for Theoretical5 Physics, Caltech, Pasadena, CA 91125, USA V V, (2) 2 Recently, motivated by a number of string theoretical Kavli Institute for the Physics and Mathematics of theJefferson Unive Physicalrse, University Laboratory, of Tokyo, Harvard Kashiwa University, 277-8583,de Cambrid Sitter Japange, MA Conjecture 02138, USA |∇ | ≥ Mp · 3 constructions with controlled approximations, it was pro- Max-Planck-Institut für Physik (Werner-Heisenberg-InsAmong Swamplandtitut), conditions, Fohringer the Ring distance 6, 80805 conjecture Munchen, chara Germanycterizes the geometry of scalar fields or 4Department of Physics, University of Wisconsin-Madison, Madison,posed WI in [1] 53706, that USA the potential for scalar fields in string and the de Sitter conjecture constrains• This allowed led potentials [Obied, Ooguri,on it. We Spodyneiko, point out a connection Vafa, ’18] between to conjecture that in ′ 5Jefferson Physical Laboratory, Harvard University, Cambridge,theory MA satisfies 02138, USA the universal bound, c the distance conjecture and a refinedparametrically version of the de controlled Sitter conjecture constructions in any parametrically of V>0 string theory solutions:min ( V ) V, (3) controlled regime of string theory by using Bousso’s covariant entropy bound. The refined version i j 2 ∇ ∇ ≤−Mp · Among Swampland conditions, theturns distance out conjecture to evade all chara counter-examplescterizes the geometry at scalar of potential scalar fieldsmaximac that have been raised. We and the de Sitter conjecture constrains allowed potentials on it. We point out a connection betweenV V, (1) ′ comment on the relation of our result to the Dine-Seiberg|∇ problem.| ≥ Mp · c ∼ �(1) >for0 some universal constants c, c > 0 of order 1,where the distance conjecture and a refined version of the de Sitter conjecture in any parametrically the left-hand side of (3) is the minimum eigenvalue of the controlled regime of string theory byPACS using numbers: Bousso’s 04.60.-m, covariant 11.25.-w entropy bound. The refined version •forThis some behavior constant is c>suggestive0oforder1,where from some earlierM is dS the constructions in turns out to evade all counter-examples at scalar potential maxima that have been raised. We p Hessian i j V in an orthonormal frame. Planckstring mass. theory1 Cosmological ([Greene, GS, implications ’15];[Danielsson, of this Van conjec- Riet, ’18] for reviews).∇ ∇ comment on the relation of our result to the Dine-Seiberg problem. Note that the conjecture is trivial if V is non-positive INTRODUCTION ture were studiedsistent in [2]. quantum The bound gravity is calledmust satisfy the de either, Sitter because (2) is satisfied, or in the limit M ,where conjecture as it excludes (meta-)stable de Sitter vacua in p PACS numbers: 04.60.-m, 11.25.-w • In [Ooguri, Palti, GS, Vafa, ’18], we arguedc that this conjecturegravity decouples.follows This refined version still→∞ excludes string theory. There have been a numberV of followV, up (2) Recently, motivated by a number of string theoreticalfrom another well-tested conjecture Mof quantum gravity,(meta-)stable and provided de Sitter vacua. papers [3–48].2 The main aim of this|∇ paper| ≥ isp · to connect constructions with controlled approximations, itthe was necessary pro- refinement: In this paper we provide evidence for the refined con- INTRODUCTION sistent quantum gravitythis conjecture must satisfyor to another either, better established swampland posed in [1] that the potential for scalar fields in string jecture only in parametrically controlled regimes of string condition, which is known as the distance conjecture′ [52]. theory satisfies the universal bound, c c theory, but it is natural to conjecture that it holds more We willV show that,V, in anyor weakmin coupling ( (2)V ) regime of stringV, (3) Recently, motivated by a number of string theoretical |∇ | ≥ M · ∇i∇j ≤−M 2 · c,generally.c′ ∼ �(1) Possible> 0 refinements of the original de Sitter c theory,3 a refinedp version of this conjecture followsp from constructions with controlled approximations, it was pro-V V, (1) conjecture have been considered in [3, 4, 6]. The refine- or the distance conjecture, combined with Bousso’s′ covari- posed in [1] that the potential for scalar fields in string|∇ | ≥ Mp · for some universal constants c, c > 0 of order ment1,where above is in essence the same as the proposal of [6].4 ant entropy bound [53] applied to an accelerating uni- theory satisfies the universal bound, thec left-hand′ side of (3) is the minimum eigenvalueNote of that the the refined version is stronger than the comple- for some constant c>0oforder1,whereMverse.is the min (p i j V ) Hessian2 V,i j V in an orthonormal(3) frame. ment of the slow roll conditions for the cosmic inflation. 1 ∇ ∇ ≤−M · ∇ ∇ Planck mass. Cosmological implicationsarXiv:1810.05506v2 [hep-th] 17 Oct 2018 of thisThe conjec- refined versionp of the de Sitter conjecture which c Note that the conjecture is trivial if V is non-positiveEffective descriptions of string theory are controlled V V,ture were studied in(1) [2]. The bound is called thewe de propose Sitter in this′ paper is stated as follows: |∇ | ≥ Mp · because (2) is satisfied, or in the limit M by,where a multitude of coupling constants, such as the string conjecture as it excludes (meta-)stablefor some universal de Sitter vacuaconstants in c, c > 0 of order 1,where p gravity decouples. This refined version still→∞coupling excludes or the volume of extra dimensions. All such string theory. There havethe been left-hand a number side of ofRefined follow (3) is up the de minimum Sitter Conjecture. eigenvalue ofApotential the V (φ) for (meta-)stable de Sitter vacua. couplings are field-dependent, and in particular, any for some constant c>0oforder1,wherepapers [3–48].M2p Theis the main aimHessian of this paperi j V isin toscalar an connect orthonormal fields in a low frame. energy effective theory of any con- 1 ∇ ∇ In this paper we provide evidence for the refinedweak con- couplings are associated with large distances in Planck mass. Cosmological implicationsthis conjecture of this conjec- to another better established swampland Note that the conjecture is trivialjecture if onlyV is in non-positive parametrically controlled regimesfield of string space. The distance conjecture [52] is about a con- ture were studied in [2]. The boundcondition, is called the which de Sitter is known as the distance conjecture [52]. because (2) is satisfied, or in thetheory, limit butMp it is natural,where to conjecture that it holdsnected more component of the moduli space of string vacua, conjecture as it excludes (meta-)stableWe willde Sitter show that, vacua in in any weak coupling regime of string →∞ 3 gravity decouples.1 This refinedgenerally. version Possible still excludes refinements of the original de Sitter string theory. There have been atheory, numbera of refined follow version up of this conjecture followsThe from power of Mp in the conjecture depends on the dimensions. (meta-)stable de Sitter vacua. conjecture have been considered in [3, 4, 6]. The refine- papers [3–48].2 The main aim of thisthe paper distance is to conjecture, connect combined with Bousso’sIn covari- this paper, for brevity, we write the formulas for the specific In this paper we providecase of 4 dimensions. evidencement above for the is in refined essence con- the same as the proposal of [6].4 this conjecture to another better establishedant entropy swampland bound [53] applied to an accelerating2 uni- 4 jecture only in parametricallyFor alternative controlledNote perspectives that regimes the on refined cosmology of string version and is microscopic stronger thanas- the comple-The refined conjecture stated in [6] reads stronger than the one condition, which is known as the distanceverse. conjecture [52]. pects of de Sitter see [49], [50] and [51]. we propose here since it was stated with the absolute-value sign 3 ment of the slow roll conditions for the cosmic inflation. 2 theory, but it is naturalIn this to paper, conjecture weak coupling that it refers holds to any more limit in any direction on η ∼∇V/V, i.e. the precise complement of the slow roll We will show that, in any weakarXiv:1810.05506v2 [hep-th] 17 Oct 2018 couplingThe regime refined of version string of the de Sitter conjecture which V generally. Possiblein refinements the space of of lowEff theective energy original scalar descriptions defields Sitter where of string a parametricall theoryy are controlledconditions. However, we have been informed by the authors of theory,3 a refined version of this conjecturewe propose follows in this from paper is stated as follows: conjecture have beencontrolled considered approximationby in a [3,multitude 4, to 6]. a The physical of coupling refine- observable constants, is possi suchble, as thethe string paper that this was unintentional as they were motivated by the distance conjecture, combined with Bousso’s covari- while the weakcoupling string coupling or the refers volume to the of4 specific extra limit dimensions. of the Allavoiding such application of the dS conjecture to maxima in poten- Refined de Sitter Conjecture.ment above is in essence the same as the proposal of [6]. ant entropy bound [53] applied to an accelerating uni- ApotentialVdilaton(φ) for field. couplings are field-dependent, and in particular,tials. any Note that the refined version is stronger than the comple- verse. scalar fields in a low energy effective theory of any con- weak couplings are associated with large distances in ment of the slow roll conditionsfield for space. the cosmic The distance inflation. conjecture [52] is about a con- arXiv:1810.05506v2 [hep-th] 17 Oct 2018 The refined version of the de Sitter conjecture which Effective descriptions of string theory are controlled we propose in this paper is stated as follows: nected component of the moduli space of string vacua, 1 by a multitude of coupling constants, such as the string The power of Mp in the conjecturecoupling depends or on the the volume dimensions. of extra dimensions. All such Refined de Sitter Conjecture. ApotentialIn this paper,V for(φ brevity,) for we write the formulas for the specific case of 4 dimensions. couplings are field-dependent, and in particular, any scalar fields in a low energy effective2 For theory alternative of any perspectives con- onweak cosmology couplings and microscopic are associatedas- 4 withThe refined large conjecture distances stated in in [6] reads stronger than the one pects of de Sitter see [49], [50] and [51]. we propose here since it was stated with the absolute-value sign 3 field space. The distance conjecture [52] is2 about a con- In this paper, weak coupling refers to any limit in any direction on ηV ∼∇V/V, i.e. the precise complement of the slow roll in the space of low energy scalarnected fields component where a parametricall of they moduliconditions. space of However, string vacua, we have been informed by the authors of controlled approximation to a physical observable is possible, the paper that this was unintentional as they were motivated by 1 The power of Mp in the conjecture dependswhile on the the weak dimensions. string coupling refers to the specific limit of the avoiding application of the dS conjecture to maxima in poten- In this paper, for brevity, we write the formulasdilaton field. for the specific tials. case of 4 dimensions. 2 For alternative perspectives on cosmology and microscopic as- 4 The refined conjecture stated in [6] reads stronger than the one pects of de Sitter see [49], [50] and [51]. we propose here since it was stated with the absolute-value sign 3 2 In this paper, weak coupling refers to any limit in any direction on ηV ∼∇V/V, i.e. the precise complement of the slow roll in the space of low energy scalar fields where a parametrically conditions. However, we have been informed by the authors of controlled approximation to a physical observable is possible, the paper that this was unintentional as they were motivated by while the weak string coupling refers to the specific limit of the avoiding application of the dS conjecture to maxima in poten- dilaton field. tials. Distance Conjecture

• Approaching any inﬁnite distance locus in moduli space, there is an inﬁnite tower of states which becomes exponentially light:

−aϕ [Ooguri, Vafa, ’06] mtower ∼ e for ϕ → ∞ • Simple example: compactiﬁcation on a circle Trivial prototypical example: compactification on a circle

−∞ ← ! ! → ∞

* ,* &' ∼ ) &++ ∼ )

• This conjecture has passed some non-trivial tests (at least for theories with 8 Highly non-trivial evidence this is general in String Theory (for 8 supercharges) supercharges) [Cecotti,’15];[Grimm, Palti, Valenzuela,‘18]; [Lee, Lerche, Weigand,‘18] [Ooguri, Vafa ‘06; … ; Cecotti ‘15; Grimm, EP, Valenzuela ‘18; Lee, Lerche, Weigand ’18; Grimm, Li, EP ‘18]

Model-independent general results – highly mathematical Distance Conjecture & Duality

• The underlying reason for this conjecture is duality: at large distance, there is a dual description in terms of the light states.

Couplings in string theory are scalar ﬁelds

Weak Coupling g → 0 ⇔ Large distance ϕ → ∞ Any weakly coupled region in string theory should have a dual description in terms of the tower of light states. CALT-TH 2018-042, IPMU 18-0164, MPP-2018-248, MAD-TH-18-06

Distance and de Sitter Conjectures on the Swampland

Hirosi Ooguri,1, 2 Eran Palti,3 Gary Shiu,4 and Cumrun Vafa5 1Walter Burke Institute for Theoretical Physics, Caltech, Pasadena, CA 91125, USA 2Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa 277-8583, Japan 3Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Fohringer Ring 6, 80805 Munchen, Germany 4Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA 5Jefferson Physical Laboratory, Harvard University, Cambridge, MA 02138, USA CALT-TH 2018-042, IPMU 18-0164, MPP-2018-248, MAD-TH-18-06 Among Swampland conditions, the distance conjecture characterizes the geometry of scalar fields and the de Sitter conjecture constrains allowed potentials on it. We point out a connection between CALT-THDistance 2018-042, and IPMU de Sitter 18-0164, Conjectures MPP-2018-248,the on MAD-TH-18- distance the Swampland conjecture06 and a refined version of the de Sitter conjecture in any parametrically controlled regime of string theory by using Bousso’s covariant entropy bound. The refined version 1, 2 3 4 5 Distance and de Sitter ConjecturesHirosi Ooguri, on theEran Swampland Palti, Gary Shiu,turnsand out Cumrun to evade Vafa all counter-examples at scalar potential maxima that have been raised. We 1Walter Burke Institute for Theoretical Physics, Caltech,comment Pasadena, on the CA relation 91125, of USA our result to the Dine-Seiberg problem. 2Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa 277-8583, Japan 1, 2 3 4 5 Hirosi Ooguri, 3Max-Planck-InstitutEran Palti, Gary für Shiu, Physik (Werner-Heisenberg-Insand Cumrun Vafa titut), FohringerPACSde numbers: Sitter Ring 6, 04.60.-m, 80805 Entropy Munchen, 11.25.-w Germany 1 4Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA Walter Burke Institute for Theoretical5 Physics, Caltech, Pasadena, CA 91125, USA 2 Jefferson Physical Laboratory, Harvard University, Cambridge, MA 02138, USA Kavli Institute for the Physics and Mathematics of the Universe, University• ofThe Tokyo, entropy Kashiwa bound 277-8583, of (quasi) Japan de Sitter space: 3 INTRODUCTION sistent quantum gravity must satisfy either, Max-Planck-Institut für Physik (Werner-Heisenberg-InsAmong Swamplandtitut), conditions, Fohringer the Ring distance 6, 80805 conjecture Munchen, chara Germanycterizes the geometry of scalar fields 4 Department of Physics, Universityand the of de Wisconsin-Madison, Sitter conjecture constrains Madison, allowed WI potentials 53706, USAon it. We point out a connection1 1 between c 5 2 V V, (2) Jefferson Physical Laboratory,the Harvard distance University,conjecture and Cambrid a refinedge, MAversion 02138, ofRecently, the USA de Sitter motivatedSGconjectureH = byR a= in number any= parametrically of string theoretical |∇ | ≥ Mp · controlled regime of string theory by using Bousso’sconstructions covariant with entropy controlled bound. approximations, TheΛ refinedV(ϕ version) it was pro- Among Swampland conditions, theturns distance out conjecture to evade all chara counter-examplescterizes the geometry at scalar of potential scalar fieldsmaxima that have been raised. We or • The towersposed of instates, [1] that which the potentialbecome forlight scalar as we fields approach in string weak coupling and the de Sitter conjecture constrainscomment allowed on potentials the relationon of it. our We result point to out the a Dine-Seiberg connection between problem. ′ the distance conjecture and a refined version of the de Sitter conjecture�→∞ in, should anytheory parametrically saturate satisfies thethe universal entropy bound,bound leading to c min ( i j V ) 2 V, (3) controlled regime of string theory byPACS using numbers: Bousso’s 04.60.-m, covariant 11.25.-w entropy bound. The refined version ∇ ∇ ≤−Mp · turns out to evade all counter-examples at scalar potential maxima that have been raised. We c V V, (1) ′ comment on the relation of our result to the Dine-Seiberg problem. |∇ | ≥ Mp · for some universal constants c, c > 0 of order 1,where INTRODUCTION sistent quantum gravity must satisfy either, the left-hand side of (3) is the minimum eigenvalue of the • PACS numbers: 04.60.-m, 11.25.-w On the other hand, this semi-classical picture of entropy bound is only for some constant c>0oforder1,wherec Mp is the Hessian i j V in an orthonormal frame. valid if quantum fluctuations1 are small, i.e., Hessian (V) not too negative.∇ ∇ Recently, motivated by a number of string theoreticalPlanck mass. CosmologicalV implicationsV, of this conjec- (2) |∇ | ≥ Mp · Note that the conjecture is trivial if V is non-positive constructions with controlled approximations,• it was pro-ture were studied in [2]. The bound is called[Ooguri, the de Palti, Sitter GS, Vafa]: INTRODUCTION sistent quantum gravityThis led must to the satisfy refined either, de Sitter conjecture because (2) is satisfied, or in the limit Mp ,where posed in [1] that the potential for scalar fields in stringconjectureor as it excludes (meta-)stable de Sitter vacua in gravity decouples. This refined version still→∞ excludes theory satisfies the universal bound, stringc theory. There have been a numberc′ of follow up V V, or2 min ( (2)V ) V, (3) (meta-)stable de Sitter vacua. Recently, motivated by a number of string theoretical papers [3–48]. The main aimi j of this paper2 is to connectc, c′ ∼ �(1) > 0 |∇ | ≥ Mp · ∇ ∇ ≤−Mp · In this paper we provide evidence for the refined con- constructions with controlled approximations, it was pro- c this conjecture to another better established swampland V V, (1) ′ jecture only in parametrically controlled regimes of string |∇ | ≥orMp · condition,for some which universal is known constants as the distancec, c > 0 conjectureof order 1 [52].,where posed in [1] that the potential for scalar fields in string theory, but it is natural to conjecture that it holds more We willthe show left-hand′ that, side in any of (3) weak is the coupling minimum regime eigenvalue of string of the theory satisfies the universal bound, 3 c generally. Possible refinements of the original de Sitter for some constant c>0oforder1,whereminM (p is theVtheory,) Hessiana refinedV, versionV in an of orthonormal this(3) conjecture frame. follows from i j 2 i j conjecture have been considered in [3, 4, 6]. The refine- Planck mass.1 Cosmological implications of this∇ conjec-∇ the≤− distanceMp · conjecture,∇ ∇ combined with Bousso’s covari- c Note that the conjecture is trivial if V is non-positive ment above is in essence the same as the proposal of [6].4 V V,ture were studied in(1) [2]. The bound is called the de Sitterant entropy′ bound [53] applied to an accelerating uni- |∇ | ≥ Mp · for some universal constants c,because c > 0 (2)of order is satisfied,1,where or in the limit Mp ,whereNote that the refined version is stronger than the comple- conjecture as it excludes (meta-)stable de Sitter vacua inverse. gravity decouples. This refined version still→∞ excludes string theory. There havethe been left-hand a number side of of follow (3) is up the minimum eigenvalue of the ment of the slow roll conditions for the cosmic inflation. arXiv:1810.05506v2 [hep-th] 17 Oct 2018 The(meta-)stable refined version de Sitter of the vacua. de Sitter conjecture which for some constant c>0oforder1,wherepapers [3–48].M2p Theis the main aimHessian of this paperi j V isin to an connect orthonormal frame. Effective descriptions of string theory are controlled 1 ∇ ∇ we proposeIn this in paperthis paper we provide is stated evidence as follows: for the refined con- Planck mass. Cosmological implicationsthis conjecture of this conjec- to another better established swampland by a multitude of coupling constants, such as the string Note that the conjecture is trivialjecture if onlyV is in non-positive parametrically controlled regimes of string ture were studied in [2]. The boundcondition, is called the which de Sitter is known as the distance conjecture [52]. coupling or the volume of extra dimensions. All such because (2) is satisfied, orRefined in thetheory, limit de but SitterMp it is Conjecture.natural,where to conjectureApotential that itV holds(φ) for more conjecture as it excludes (meta-)stableWe will de Sitter show that, vacua in in any weak coupling regime of string →∞ couplings are field-dependent, and in particular, any gravity decouples. Thisscalar refinedgenerally. fields version in a Possible low still energy excludes refinements effective of theory the original of any de con- Sitter string theory. There have been atheory, number3 a of refined follow version up of this conjecture follows from weak couplings are associated with large distances in (meta-)stable de Sitter vacua. conjecture have been considered in [3, 4, 6]. The refine- papers [3–48].2 The main aim of thisthe paper distance is to conjecture, connect combined with Bousso’s covari- field space. The distance conjecture [52] is about a con- In this paper we provide evidencement above for the is in refined essence con- the same as the proposal of [6].4 this conjecture to another better establishedant entropy swampland bound [53] applied to an accelerating uni- nected component of the moduli space of string vacua, jecture only in parametrically1 controlledNote that regimes the refined of stringversion is stronger than the comple- condition, which is known as the distanceverse. conjecture [52]. The power of Mp in the conjecture depends on the dimensions. theory, but it is natural to conjecturement of that the slow it holds roll conditions more for the cosmic inflation.

arXiv:1810.05506v2 [hep-th] 17 Oct 2018 In this paper, for brevity, we write the formulas for the specific We will show that, in any weak couplingThe regime refined of version string of the de Sitter conjecture which Effective descriptions of string theory are controlled 3 generally. Possible refinementscase of of 4 the dimensions. original de Sitter theory, a refined version of this conjecturewe propose follows in this from paper is stated as follows: 2 4 conjecture have been consideredForby alternative in a multitude [3, 4, perspectives 6]. The of coupling refine- on cosmology constants, and such microscopic as theas- string The refined conjecture stated in [6] reads stronger than the one the distance conjecture, combined with Bousso’s covari- pectscoupling of de Sitter or seethe [49], volume [50] and of4 [51]. extra dimensions. All such we propose here since it was stated with the absolute-value sign Refined de Sitter Conjecture.ment above is in essence the3 same as the proposal of [6]. ∼∇2 ant entropy bound [53] applied to an accelerating uni- ApotentialV (φ) for In thiscouplings paper, weak are coupling field-dependent, refers to any and limit in in particular, any direction any on ηV V/V, i.e. the precise complement of the slow roll scalar fields in a low energyNote effective that theory the refined of any version con- in is the stronger space of than low energy the comple- scalar fields where a parametrically conditions. However, we have been informed by the authors of verse. controlledweak couplings approximation are to associated a physical with observable large is distances possible, in the paper that this was unintentional as they were motivated by ment of the slow roll conditionsfield for space. the cosmic The distance inflation. conjecture [52] is about a con- arXiv:1810.05506v2 [hep-th] 17 Oct 2018 while the weak string coupling refers to the specific limit of the avoiding application of the dS conjecture to maxima in poten- The refined version of the de Sitter conjecture which Effective descriptions of string theory are controlled we propose in this paper is stated as follows: dilatonnected field. component of the moduli space of string vacua, tials. 1 by a multitude of coupling constants, such as the string The power of Mp in the conjecturecoupling depends or on the the volume dimensions. of extra dimensions. All such Refined de Sitter Conjecture. ApotentialIn this paper,V for(φ brevity,) for we write the formulas for the specific case of 4 dimensions. couplings are field-dependent, and in particular, any scalar fields in a low energy effective2 For theory alternative of any perspectives con- onweak cosmology couplings and microscopic are associatedas- 4 withThe refined large conjecture distances stated in in [6] reads stronger than the one pects of de Sitter see [49], [50] and [51]. we propose here since it was stated with the absolute-value sign 3 field space. The distance conjecture [52] is2 about a con- In this paper, weak coupling refers to any limit in any direction on ηV ∼∇V/V, i.e. the precise complement of the slow roll in the space of low energy scalarnected fields component where a parametricall of they moduliconditions. space of However, string vacua, we have been informed by the authors of controlled approximation to a physical observable is possible, the paper that this was unintentional as they were motivated by 1 The power of Mp in the conjecture dependswhile on the the weak dimensions. string coupling refers to the specific limit of the avoiding application of the dS conjecture to maxima in poten- In this paper, for brevity, we write the formulasdilaton field. for the specific tials. case of 4 dimensions. 2 For alternative perspectives on cosmology and microscopic as- 4 The refined conjecture stated in [6] reads stronger than the one pects of de Sitter see [49], [50] and [51]. we propose here since it was stated with the absolute-value sign 3 2 In this paper, weak coupling refers to any limit in any direction on ηV ∼∇V/V, i.e. the precise complement of the slow roll in the space of low energy scalar fields where a parametrically conditions. However, we have been informed by the authors of controlled approximation to a physical observable is possible, the paper that this was unintentional as they were motivated by while the weak string coupling refers to the specific limit of the avoiding application of the dS conjecture to maxima in poten- dilaton field. tials. CALT-TH 2018-042, IPMU 18-0164, MPP-2018-248, MAD-TH-18-06

Distance and de Sitter Conjectures on the Swampland

• While not our motivation, our reﬁned de Sitter conjecture can evade some counterexamples [Denef, Hebecker, Wrase];[Conlon];[Murayama, Yamazaki, Yanagida]; [Choi, Chway,Shin];[Hamaguchi, Ibe, Moroi] to the original de Sitter conjecture.

• The top of the Higgs potential:

10−55 1035 |∇V| ∼ V min(∇ ∇ V) ∼ − V i j 2 MPl MPl

• The top of the potential for the pion or QCD axion 1 min(∇ ∇ V) ∼ − V i j f 2 The WGC for axions gives f ≤ MPl String Theory and Data Science

About 25 papers written since 2017, ranging from using topological data analysis to analyze the structure of the landscape [Cole, GS ’17, ’18] to using machine learning to search for phenomenologically interesting string vacua [Ruhle, ’17]; [Mutter, Parr, Vaudrevange, ’18];[Halverson, Nelson, Ruhle, ’19] 5 international meetings on this theme have taken place and more to come: BostonApplication: (11/17), Munich (03/18), Sanya (06/18), https://www.microsoftevents.com/profile/form/index.cfm?PKformID=0x5969440abcdTrieste (12/18), Seattle (04/19) Summary Summary

• String pheno continues to be a vital ﬁeld that aims at extracting fundamental predictions on low energy physics from string theory/quantum gravity.

• The Swampland program attempts to clarify the formulation, motivation and applications of several consistency criteria: • No global symmetries -> Mini-charged DM. • Weak Gravity Conjecture -> Large field (natural) inflation, Fuzzy DM • Large distances in moduli space -> Axion monodromy inflation. • Instability of non-SUSY AdS -> Neutrino physics? [Ooguri, Vafa, ’16]; [Ibanez, Martin-Lozano, Valenzuela, ’17];[Hamada, GS, ’17] • No dS -> Inflation, CC, quintessence

• Despite recent intense effort, much work remains to be done to fully understand the origin and consequences of these conjectures.

• Budding effort in String Theory ∩ Data Science.