Swampland Conjectures

Pablo Soler - Heidelberg ITP

Strings and Fields ’19 - YITP Kyoto String phenomenology & the swampland `

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Field theory (in 10d)

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4d EFT & phenomenology

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4d EFT & phenomenology

String phenomenology explores compactiﬁcation spaces X 6 d that reproduce the SM and interesting BSM scenarios. String Pheno and the Swampland

500 • String theory admits a vast number & 10 of 4d solutions: “the string landscape” Douglas ‘03

• Two main traditional approaches to string phenomenology:

• What is generic? Axions, moduli,…

• What is possible? The SM, low energy SUSY, …

• Recently, a novel perspective has emerged:

• What is impossible? “The swampland”

Vafa ’05; Ooguri, Vafa ’06;…… See Palti ’19 for a review String Pheno and the Swampland

272000 • String theory admits a vast number & 10 of 4d solutions: “the string landscape” Braun, Watari ’15; Taylor, Wang ’15

• Two main traditional approaches to string phenomenology:

• What is generic? Axions, moduli,…

• What is possible? The SM, low energy SUSY, …

• Recently, a novel perspective has emerged:

• What is impossible? “The swampland”

Vafa ’05; Ooguri, Vafa ’06;…… See Palti ’19 for a review String Pheno and the Swampland

String Landscape

String Pheno and the Swampland

String Landscape

BSM Scenarios String Pheno and the Swampland

String Landscape

BSM Scenarios

Our World String Pheno and the Swampland

Swampland

String Landscape

BSM Scenarios

Our World String Pheno and the Swampland

• What properties distinguish landscape and swampland?

Swampland conjectures

• How do we test them?

String tests

Quantum gravity (black hole) arguments

• What are the implications for phenomenology? Are there BSM proposals that live in the swampland? Outline

• No Global Symmetries

• The Weak Gravity Conjecture

‣ Axion-WGC and axion inﬂation

• The non-SUSY AdS conjecture

• The swampland distance conjecture

• The no de-Sitter conjecture

• The AdS distance conjecture Outline

• No Global Symmetries rigorous

• The Weak Gravity Conjecture

‣ Axion-WGC and axion inﬂation

• The non-SUSY AdS conjecture

• The swampland distance conjecture

• The no de-Sitter conjecture

• The AdS distance conjecture speculative Disclaimer

Many of the ideas in this talk are still quite speculative and controversial Quantum Gravity and Global Symmetries QG and Global Symmetries

• Global symmetries are expected to be violated in QG:

Q, M

Q, Mp

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

➡ Inﬁnite number of states (remnants) with m . Mp ➡ Breakdown of EFT (e.g. at ﬁnite temperature the density of states blows up) Susskind ‘95

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

• Proven in (perturbative) string theory and in AdS/CFT.

Banks, Dixon ’88; Harlow, Ooguri ‘18 QG and Global Symmetries

• Pheno application: mini-charged Dark Matter

What if Dark Matter was not electrically neutral?

1 = F F µ⌫ + A (J µ + ✏ J µ ) L 4e µ⌫ µ SM DM

• Mini-charge: ε << 1

• The SM charges are quantized (in units of e ). DM charges are proportional to ✏ e

• Imagine ✏ is irrational: charges are not quantized.

SM 0 1 2 3 4 5 6 7 8 9 QG and Global Symmetries

• Pheno application: mini-charged Dark Matter

What if Dark Matter was not electrically neutral?

1 = F F µ⌫ + A (J µ + ✏ J µ ) L 4e µ⌫ µ SM DM

• Mini-charge: ε << 1

• The SM charges are quantized (in units of e ). DM charges are proportional to ✏ e

• Imagine ✏ is irrational: charges are not quantized.

SM 0 1 2 3 4 5 6 7 8 9 DM QG and Global Symmetries

• Pheno application: mini-charged Dark Matter

What if Dark Matter was not electrically neutral?

1 = F F µ⌫ + A (J µ + ✏ J µ ) L 4e µ⌫ µ SM DM

• Problem: the theory contains an exact global symm.

• Gauge symmetry: • Global symmetry:

Aµ Aµ + e @µ↵ Aµ Aµ ! i↵ ! SM e SM SM SM ! i✏↵ ! i e DM e DM DM ! DM ! Every gauge invariant operator, is invariant under global -transformations Banks, Seiberg ‘10 QG and Global Symmetries

• Pheno application: mini-charged Dark Matter

What if Dark Matter was not electrically neutral?

1 = F F µ⌫ + A (J µ + ✏ J µ ) L 4e µ⌫ µ SM DM

• Conclusion: simplest minicharged DM models Swampland 2 • Possible ways out:

- Small rational charges: ✏ Q Unnatural 2 - Gauge extra global symmetry = New massless gauge boson ) 1 1 = F F µ⌫ F˜ F˜µ⌫ + A (J µ + ✏ J µ )+A˜ J µ L 4e µ⌫ 4˜e µ⌫ µ SM DM µ DM

Holdom ’86; Shiu, PS, Ye ‘13 The Weak Gravity Conjecture The Weak Gravity Conjecture

• We have argued that global symmetries are in conﬂict with Quantum Gravity

• Gauge symmetry at g=0 ⇒ Global symmetry

• It is not unreasonable to expect problems for gauge theories in the weak coupling limit: g -> 0

• When do things go wrong? How? … The Weak Gravity Conjecture

• Take U(1) gauge theory with only one charged ﬁeld 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 states are exactly stable

• These may be problematic*: in order to avoid them, one postulates the existence of some particle with

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M MAAAB6HicbVA9SwNBEJ2LXzF+RS1tFoNgFe5E0MIiYGMjJGA+IDnC3mYuWbO3d+zuCeHIL7CxUMTWn2Tnv3GTXKGJDwYe780wMy9IBNfGdb+dwtr6xuZWcbu0s7u3f1A+PGrpOFUMmywWseoEVKPgEpuGG4GdRCGNAoHtYHw789tPqDSP5YOZJOhHdCh5yBk1Vmrc98sVt+rOQVaJl5MK5Kj3y1+9QczSCKVhgmrd9dzE+BlVhjOB01Iv1ZhQNqZD7FoqaYTaz+aHTsmZVQYkjJUtachc/T2R0UjrSRTYzoiakV72ZuJ/Xjc14bWfcZmkBiVbLApTQUxMZl+TAVfIjJhYQpni9lbCRlRRZmw2JRuCt/zyKmldVD236jUuK7WbPI4inMApnIMHV1CDO6hDExggPMMrvDmPzovz7nwsWgtOPnMMf+B8/gCjP4zL

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• “Mild” - WGC (does not constrain low energy EFT) The Weak Gravity Conjecture

• “Strong” - WGC (important pheno implications) The Weak Gravity Conjecture

• String theory seems to satisfy stronger versions of the WGC (“sub-lattice or tower WGC”) Evidence for the WGC

Unitarity/ BH Casuality Thermo

Cheung, Remmen, ’14; Cottrell, Shiu, PS, ’16; Andriolo, Junghans, Noumi, Shiu,’18; Hebecker, PS, ’17; Hamada, Noumi, Shiu, ’18; Cheung, Liu, Remmen, ’18, ‘19; Chen, Huang, Noumi, Wen ’19; WGC Hamada, Noumi, Shiu, ’18; … Bellazzini, Lewandowski, Serra ’19…

Nakayama, Nomura, ’15; Harlow, ’15; Horowitz, Santos, Way, ’16; Montero, Shiu, PS ‘16; Montero ‘18… Crisford, Horowitz, Santos, ’17; …

Cosmic Holography Censorship The WGC for axions WGC and axions

• U(1) gauge theory in 5d compactiﬁed on a circle to 4d:

5d theory 4d theory

A (x, x ) (A (x), (x))

Fields 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 M 4 µ !

5 1 MN 4 1 µ⌫ 1 µ Action S = d x FMNF d x Fµ⌫ F @µ@ 4g2 ! 4g2 2 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 Z 5 Z ✓ 4 ◆ Symmetries A A + @ A A + @ , + c 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 M ⇠ M M ! µ ⇠ µ µ ⇠ φ is an axion How is V(φ) generated?

Charged matter AAAB+HicbVBNS8NAEN3Ur1o/GvXoZbEInkoigh48FLx4rGA/oA1ls92kSze7YXei1NBf4sWDIl79Kd78N27bHLT1wcDjvRlm5oWp4AY879spra1vbG6Vtys7u3v7VffgsG1UpilrUSWU7obEMMElawEHwbqpZiQJBeuE45uZ33lg2nAl72GSsiAhseQRpwSsNHCrfaFkrHk8AqK1ehy4Na/uzYFXiV+QGirQHLhf/aGiWcIkUEGM6fleCkFONHAq2LTSzwxLCR2TmPUslSRhJsjnh0/xqVWGOFLalgQ8V39P5CQxZpKEtjMhMDLL3kz8z+tlEF0FOZdpBkzSxaIoExgUnqWAh1wzCmJiCaGa21sxHRFNKNisKjYEf/nlVdI+r/te3b+7qDWuizjK6BidoDPko0vUQLeoiVqIogw9o1f05jw5L86787FoLTnFzBH6A+fzB3Bqk5A=sha1_base64="hP+6LrUf2d3tZaldqaQQvEKMXyw=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odBu3wMYA6nMMFXEEIN3AHD9CBLghI4BXevYn35n2suqp569LO4I+8zx84xIo4sha1_base64="1fSSaQaXgkiI4mg1T76dIElkmdI=">AAAB7XicbZBLSwMxFIXv1Fet1Y5u3QSL4KrMuNGl4MZlBfuAtpRMmpmGZpIhuaPUob/EjQtF/Dvu/Demj4W2Hgh8nJNwb06USWExCL690tb2zu5eeb9yUD08qvnH1bbVuWG8xbTUphtRy6VQvIUCJe9mhtM0krwTTW7neeeRGyu0esBpxgcpTZSIBaPorKFf60utEiOSMVJj9NPQrweNYCGyCeEK6rBSc+h/9Uea5SlXyCS1thcGGQ4KalAwyWeVfm55RtmEJrznUNGU20GxWHxGzp0zIrE27igkC/f3i4Km1k7TyN1MKY7tejY3/8t6OcbXg0KoLEeu2HJQnEuCmsxbICNhOEM5dUCZEW5XwsbUUIauq4orIVz/8ia0Lxth0AjvAyjDKZzBBYRwBTdwB01oAYMcXuAN3r1n79X7WNZV8la9ncAfeZ8/F9SSMw==sha1_base64="PecRLNpqrhz1a/qN2e8R3dp43vU=">AAAB+HicbVA9SwNBEJ3zM8aPnFraHAbBKtzZaGERsLGMYD4gOcLeZu+yZG/32J1TYsgvsbFQxNafYue/cZNcoYkPBh7vzTAzL8oEN+j7387a+sbm1nZpp7y7t39QcQ+PWkblmrImVULpTkQME1yyJnIUrJNpRtJIsHY0upn57QemDVfyHscZC1OSSB5zStBKfbfSE0ommidDJFqrx75b9Wv+HN4qCQpShQKNvvvVGyiap0wiFcSYbuBnGE6IRk4Fm5Z7uWEZoSOSsK6lkqTMhJP54VPvzCoDL1balkRvrv6emJDUmHEa2c6U4NAsezPxP6+bY3wVTrjMcmSSLhbFufBQebMUvAHXjKIYW0Ko5vZWjw6JJhRtVmUbQrD88ippXdQCvxbc+dX6dRFHCU7gFM4hgEuowy00oAkUcniGV3hznpwX5935WLSuOcXMMfyB8/kDbyqTjA== Charged matter + Instantons ! ALPs in string theory: a toy model

• Consider a 5d particle with mass ‘m5’ and charge ‘q5’ whose (Euclidean) worldline wraps the compact dimension

• This particle sources the axion and is localized to a point in 4d spacetime, i.e. it is an instanton:

S Sinst =2⇡Rm5 V () e inst cos f f = q5p2⇡R 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 ⇠ ✓ ◆ • 3 The 5d WGC for charged particles m 5

f S M · inst  p Phenomenological application:

Axion inﬂation WGC and axion inﬂation

UV sensitivity of large field inflation: >MP WGC and axion inflation

• Inﬂation with axions:

S kS k V () e inst 1 cos + e inst 1 cos / f f  ✓ ◆ k>X1  ✓ ◆

• Simplest natural inﬂation: slow roll and pert. control

Sinst f>M ,e 1= f Sinst >Mp p ⌧ ) · Non-SUSY AdS conjecture Non-SUSY AdS conjecture

• Extremal branes contain AdSp ( x S ) factors in their near horizon geometries supported by ﬂux

• The WGC implies that such backgrounds must be unstable against emission of super-extremal WGC-states.

• WGC corollary: non-SUSY AdS spaces supported by ﬂux are unstable

• This conclusion lead [Ooguri, Vafa ’16] to conjecture

• Non-SUSY AdS conjecture: any non-SUSY AdS space must exhibit some instability

• This would have important implications for non-SUSY AdS/CFT and under further assumptions for particle (neutrino) physics

Ibanez, Martin-Lozano, Valenzuela ’17; Hamada, Shiu ’17; Gonzalo, (Herraez), Ibanez ‘18 The swampland distance conjecture Swampland distance conjecture

• String compactiﬁcations contain numerous scalar ﬁelds (moduli) whose vev control the couplings of the theory.

• Consider a circle compactiﬁcation to d-dimensions of perturbative string theory (Mp=1)

• Canonically normalized radius modulus φ is RAAAB/XicdVDJSgNBEO2JW4xbXG5eGoPgKfQEowl4CHjxGMUskBlDT6eSNOlZ6O4R4hD8FS8eFPHqf3jzb+wkI6jog4LHe1VU1fMiwZUm5MPKLCwuLa9kV3Nr6xubW/ntnaYKY8mgwUIRyrZHFQgeQENzLaAdSaC+J6Dljc6nfusWpOJhcK3HEbg+HQS8zxnVRurm964cxX0MN4njgabYiYZ80s0XSJHMgEmxVCbVypSUiV09sbGdWgWUot7Nvzu9kMU+BJoJqlTHJpF2Eyo1ZwImOSdWEFE2ogPoGBpQH5SbzK6f4EOj9HA/lKYCjWfq94mE+kqNfc90+lQP1W9vKv7ldWLdr7gJD6JYQ8Dmi/qxwDrE0yhwj0tgWowNoUxycytmQyop0yawnAnh61P8P2mWijYp2pfHhdpZGkcW7aMDdIRsdIpq6ALVUQMxdIce0BN6tu6tR+vFep23Zqx0Zhf9gPX2CVZTlSI= e with β~Ο(1) ⇠ • Moving in moduli φ-space changes the spectrum of the theory 2 2 d 2 2 k 1 2 ↵ KK modes: M k e k ⇠ R R ⇠ 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 ✓ ◆ ✓ ◆ 2 2 2 d 2 2 ↵ (↵ (1)) M (wR) R w e AAACAXicbVDLSgNBEJyNrxhfq14EL4NBSC5hR+LrFvDizQgmEbIh9E5mkyGzD2ZmhbDEi7/ixYMiXv0Lb/6Nk2RBjRY0FFXddHd5seBKO86nlVtYXFpeya8W1tY3Nrfs7Z2mihJJWYNGIpK3HigmeMgammvBbmPJIPAEa3nDi4nfumNS8Si80aOYdQLoh9znFLSRuvZeyQURD8BVPMCpS0Hgq3GJlMtdu+hUjh1yfkKwU3Gm+CYkI0WUod61P9xeRJOAhZoKUKpNnFh3UpCaU8HGBTdRLAY6hD5rGxpCwFQnnX4wxodG6WE/kqZCjafqz4kUAqVGgWc6A9ADNe9NxP+8dqL9s07KwzjRLKSzRX4isI7wJA7c45JRLUaGAJXc3IrpACRQbUIrmBDI/Mt/SfOoQpwKua4Wa9UsjjzaRweohAg6RTV0ieqogSi6R4/oGb1YD9aT9Wq9zVpzVjazi37Bev8CfveVkA== Winding modes: 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 w ⇠ ⇠ ⇠ O

•

AAAB+HicbVBNS8NAEJ3Ur1o/GvXoJVgEL5ZEBD14KHjxWMF+QBPKZrtpl242YXcixNJf4sWDIl79Kd78N27bHLT1wcDjvRlm5oWp4Bpd99sqra1vbG6Vtys7u3v7VfvgsK2TTFHWoolIVDckmgkuWQs5CtZNFSNxKFgnHN/O/M4jU5on8gHzlAUxGUoecUrQSH276qcj7mPinPtcRpj37Zpbd+dwVolXkBoUaPbtL3+Q0CxmEqkgWvc8N8VgQhRyKti04meapYSOyZD1DJUkZjqYzA+fOqdGGThRokxJdObq74kJibXO49B0xgRHetmbif95vQyj62DCZZohk3SxKMqEYx6dpeAMuGIURW4IoYqbWx06IopQNFlVTAje8surpH1R99y6d39Za9wUcZThGE7gDDy4ggbcQRNaQCGDZ3iFN+vJerHerY9Fa8kqZo7gD6zPH3B2kuo=

Both at large ( AAAB9XicbVBNS8NAEJ34WetX1aOXxSJ4KokIevBQ8OKxgv2AJpbNdtMu3WzC7kQJpf/DiwdFvPpfvPlv3LY5aOuDgcd7M8zMC1MpDLrut7Oyura+sVnaKm/v7O7tVw4OWybJNONNlshEd0JquBSKN1Gg5J1UcxqHkrfD0c3Ubz9ybUSi7jFPeRDTgRKRYBSt9OCnQ+FjQnyhIsx7lapbc2cgy8QrSBUKNHqVL7+fsCzmCpmkxnQ9N8VgTDUKJvmk7GeGp5SN6IB3LVU05iYYz66ekFOr9EmUaFsKyUz9PTGmsTF5HNrOmOLQLHpT8T+vm2F0FYyFSjPkis0XRZkk9s9pBKQvNGcoc0so08LeStiQasrQBlW2IXiLLy+T1nnNc2ve3UW1fl3EUYJjOIEz8OAS6nALDWgCAw3P8ApvzpPz4rw7H/PWFaeYOYI/cD5/AIt2koI= ) and small ( ) radius there is an !1 !1 inﬁnite tower of states that becomes exponentially light Swampland distance conjecture

• Such behaviour is very generic in string theory, leading to

Swampland Distance Conjecture: given two points ‘p’ and ‘q’ in moduli space separated by a distance d M

AAAB9XicdVDLSsNAFJ3UV62vqks3g0VwIWFSrLbgouDGjVDBPqCNYTKZtEMnD2cmSgn9DzcuFHHrv7jzb5y0EVT0wIXDOfdy7z1uzJlUCH0YhYXFpeWV4mppbX1jc6u8vdORUSIIbZOIR6LnYkk5C2lbMcVpLxYUBy6nXXd8nvndOyoki8JrNYmpHeBhyHxGsNLSjeek8dHtdDAcwksndsoVZKIZIDKrNdSoZ6SGrMaJBa3cqoAcLaf8PvAikgQ0VIRjKfsWipWdYqEY4XRaGiSSxpiM8ZD2NQ1xQKWdzq6ewgOteNCPhK5QwZn6fSLFgZSTwNWdAVYj+dvLxL+8fqL8up2yME4UDcl8kZ9wqCKYRQA9JihRfKIJJoLpWyEZYYGJ0kGVdAhfn8L/SadqWsi0ro4rzbM8jiLYA/vgEFjgFDTBBWiBNiBAgAfwBJ6Ne+PReDFe560FI5/ZBT9gvH0CTZ+SXA== p,q p there exists an inﬁnite tower of states with mass scale

d ↵ p,q M(q)

AAACEXicdVDLSgMxFM34tr5GXboJFqEFLRmxPsBFwY2bgoJ9QFuHTJppg5mZNMkIZZhfcOOvuHGhiFt37vwb03YEFT1w4XDOvdx7jyc4UxqhD2tqemZ2bn5hMbe0vLK6Zq9v1FUUS0JrJOKRbHpYUc5CWtNMc9oUkuLA47Th3ZyN/MYtlYpF4ZUeCtoJcC9kPiNYG8m1C9XCoHhaLYgivU722piLPoZtX2KSdN1E7A7SNKm6Ik1dO49KaAyISvtldHI8ImXknBw60MmsPMhw4drv7W5E4oCGmnCsVMtBQncSLDUjnKa5dqyowOQG92jL0BAHVHWS8Ucp3DFKF/qRNBVqOFa/TyQ4UGoYeKYzwLqvfnsj8S+vFWv/uJOwUMSahmSyyI851BEcxQO7TFKi+dAQTCQzt0LSxyYObULMmRC+PoX/k/p+yUEl5/IgX6lkcSyALbANCsABR6ACzsEFqAEC7sADeALP1r31aL1Yr5PWKSub2QQ/YL19AqV4nPY=

with ↵ (1) Ooguri, Vafa ‘16 AAAB/3icdVDJSgNBEO1xjXGLCl68NAYhXoaeYDQBDwEv3oxgFsgMoabTSZr0LHT3CGHMwV/x4kERr/6GN//GziKo6IOCx3tVVNXzY8GVJuTDWlhcWl5Zzaxl1zc2t7ZzO7sNFSWSsjqNRCRbPigmeMjqmmvBWrFkEPiCNf3hxcRv3jKpeBTe6FHMvAD6Ie9xCtpIndy+CyIegKt4gFOXgsBX44Jz3MnliU2mwMQulkilPCEl4lROHezMrTyao9bJvbvdiCYBCzUVoFTbIbH2UpCaU8HGWTdRLAY6hD5rGxpCwJSXTu8f4yOjdHEvkqZCjafq94kUAqVGgW86A9AD9dubiH957UT3yl7KwzjRLKSzRb1EYB3hSRi4yyWjWowMASq5uRXTAUig2kSWNSF8fYr/J42i7RDbuT7JV8/ncWTQATpEBeSgM1RFl6iG6oiiO/SAntCzdW89Wi/W66x1wZrP7KEfsN4+AdIolUs= ⇠ O Swampland distance conjecture

• Remarks • The swampland distance conjecture has been conﬁrmed

extensively in asymptotic limits of moduli space dAAAB8nicdVBNSwMxFMzWr1q/qh69BIvgackWqy14KHjxWMHaQltKNpttQ7PZJXkrlKU/w4sHRbz6a7z5b0zbFVR0IDDMvEfejJ9IYYCQD6ewsrq2vlHcLG1t7+zulfcP7kycasbbLJax7vrUcCkUb4MAybuJ5jTyJe/4k6u537nn2ohY3cI04YOIjpQIBaNgpV7Qhxj3hQphOixXiEsWwMSt1kijPic14jXOPezlVgXlaA3L7/0gZmnEFTBJjel5JIFBRjUIJvms1E8NTyib0BHvWapoxM0gW5w8wydWCXAYa/sU4IX6fSOjkTHTyLeTEYWx+e3Nxb+8XgphfZAJlaTAFVt+FKYS25zz/DgQmjOQU0so08LeitmYasrAtlSyJXwlxf+Tu6rrEde7Oas0L/M6iugIHaNT5KEL1ETXqIXaiKEYPaAn9OyA8+i8OK/L0YKT7xyiH3DePgF1NpFZ !1 Grimm, Palti, Valenzuela ’18; Grimm, Li, Palti ’18, Corvilain, Grimm, Valenzuela ’18; Blumenhagen, Kläwer, Schlechter, Wolf ’18; Hebecker, Junghans, Schachner ’18; Joshi, Klemm ’19; Lee, Lerche, Weigand ’19;…

• The tower of light states is expected to arise already when d M AAAB9HicdVDLSsNAFJ3UV62vqks3g0VwFSbFagsuCm7cCBXsA9pQJpNJO3QyiTOTQgn9DjcuFHHrx7jzb5y0EVT0wIXDOfdy7z1ezJnSCH1YhZXVtfWN4mZpa3tnd6+8f9BRUSIJbZOIR7LnYUU5E7Stmea0F0uKQ4/Trje5yvzulErFInGnZzF1QzwSLGAEayO5PhyMtHFDeDOMh+UKstECENnVGmrUM1JDTuPcgU5uVUCO1rD8PvAjkoRUaMKxUn0HxdpNsdSMcDovDRJFY0wmeET7hgocUuWmi6Pn8MQoPgwiaUpouFC/T6Q4VGoWeqYzxHqsfnuZ+JfXT3RQd1Mm4kRTQZaLgoRDHcEsAegzSYnmM0MwkczcCskYS0y0yalkQvj6FP5POlXbQbZze1ZpXuZxFMEROAanwAEXoAmuQQu0AQH34AE8gWdraj1aL9brsrVg5TOH4Aest09lpZHW & p “Refined distance • It is expected to hold in the presence of conjecture” a potential V(φ) Baume, Palti ’16; Klaewer, Palti ’16 • If correct, EFT cannot be trusted upon trans-Planckian displacements of scalar fields • Would strongly constrain models of large field inflation Ongoing debate dS vacua and the swampland dS and the swampland

• It is notoriously difﬁcult to obtain string dS vacua.

• The difﬁculty can be traced back to the Dine-Seiberg problem:

In string theory, there are no free parameters: coupling constants are vevs of scalar ﬁelds (moduli), e.g. gs = e At weak coupling ( ), vacuum energy vanishes !1

V () • V>0: runaway (quintessence?) V () ae + ... ⇠ • V=0: ﬂat (massless )

• V<0: roll to strong coupling

Dine, Seiberg ’85 dS and the swampland

• It is notoriously difﬁcult to obtain string dS vacua.

• The difﬁculty can be traced back to the Dine-Seiberg problem:

In string theory, there are no free parameters: coupling constants are vevs of scalar ﬁelds (moduli), e.g. gs = e At weak coupling ( ), vacuum energy vanishes !1

V ()

• No vacuum (either AdS, Mink, V () ae + ... ⇠ or dS) at parametrically weak coupling exists!

Dine, Seiberg ’85 dS and the swampland

• To ﬁnd a minimum, one needs higher order corrections in the potential, but then perturbativity is endangered

2 a V ()= ae + be + ... = g = e 0 = ) s 2b

• Option 1: gs ~ a/b~1 strong coupling (no control)!

V () • Option 2: gs ~ a/b << 1 AdS at small coupling (‘non- parametric’ control)

dS and the swampland

• To ﬁnd a minimum, one needs higher order corrections in the potential, but then perturbativity is endangered

2 3 V ()=ae be + ce + ...

• With one more term, one can obtain potentials with dS minima at gs << 1. Not ideal, but who said it should be? V ()

Moduli stabilization and constructions of vacua (AdS or dS) exploit this mechanism

GKP ‘01, KKLT ‘03, LVS ‘05 dS and the swampland

• Recent suggestion: in every direction in moduli space, the potential must satisfy asymptotically

V () ↵ V ↵ (1) , |r | ⇠ O !1 Obied, Ooguri, Spodyneiko, Vafa ‘18 This behaviour arises naturally in string theory, and is required

asymptotically by the distance conjecture. Ooguri, Palti, Shiu, Vafa ‘18

• De Sitter swampland conjecture: this must hold (with minor qualiﬁcations) throughout moduli space, forbidding dS vacua. dS vacua (KKLT, LVS) vs. dS swampland conjecture Necessarily complicated Simple but speculative Vacuum energy Quintessence

Lively ongoing debate AdS distance conjecture AdS distance conjecture

• The most rigorously stablished AdS solutions of string theory take the form AdS X , with the radius of AdS of the same order as AAAB+HicbVBNS8NAEN3Ur1o/GvXoZbEInkoiguKp4sVjRfsBbQibzaZdutnE3YlQQ3+JFw+KePWnePPfuG1z0NYHA4/3ZpiZF6SCa3Ccb6u0srq2vlHerGxt7+xW7b39tk4yRVmLJiJR3YBoJrhkLeAgWDdVjMSBYJ1gdD31O49MaZ7IexinzIvJQPKIUwJG8u3qVXjnp33gMdO46z/4ds2pOzPgZeIWpIYKNH37qx8mNIuZBCqI1j3XScHLiQJOBZtU+plmKaEjMmA9QyUxi7x8dvgEHxslxFGiTEnAM/X3RE5ircdxYDpjAkO96E3F/7xeBtGFl3OZZsAknS+KMoEhwdMUcMgVoyDGhhCquLkV0yFRhILJqmJCcBdfXibt07rr1N3bs1rjsoijjA7RETpBLjpHDXSDmqiFKMrQM3pFb9aT9WK9Wx/z1pJVzBygP7A+fwA7pZLG p ⇥ q the radius of X (as in AdS5 x S5)

There is no gap between Λ and the massive KK states

Λ -> 0 corresponds to Vol(X) -> ∞ . This is an inﬁnite distance in moduli space, and comes with a tower of light states

• AdS distance conjecture

Any theory of Quantum Gravity in AdS spacetime contains a tower of states with mass scale (Mp=1) ↵ ( ↵ =1 / 2 in SUSY) m ⇤ AAAB8nicdVDLSgMxFM34rPVVdekmWARXY1KstoJQcOOygn3AdCiZNNOGZiZDkhFK6We4caGIW7/GnX9jph1BRQ9cOJxzL/feEySCa4PQh7O0vLK6tl7YKG5ube/slvb221qmirIWlUKqbkA0EzxmLcONYN1EMRIFgnWC8XXmd+6Z0lzGd2aSMD8iw5iHnBJjJa9HRDIi8AqfVvqlMnLRHBC5lSqq1zJSRbh+jiHOrTLI0eyX3nsDSdOIxYYKorWHUWL8KVGGU8FmxV6qWULomAyZZ2lMIqb96fzkGTy2ygCGUtmKDZyr3yemJNJ6EgW2MyJmpH97mfiX56UmrPlTHiepYTFdLApTAY2E2f9wwBWjRkwsIVRxeyukI6IINTalog3h61P4P2lXXIxcfHtWblzmcRTAITgCJwCDC9AAN6AJWoACCR7AE3h2jPPovDivi9YlJ585AD/gvH0C+6WQXw== AAAB/3icdVDLSgMxFM3UV62vUcGNm2ARXJVMsdruCm5cuKhgH9Cp5U6atqHJzJBkhNJ24a+4caGIW3/DnX9j+hBU9EDgcM493JsTxIJrQ8iHk1paXlldS69nNja3tnfc3b2ajhJFWZVGIlKNADQTPGRVw41gjVgxkIFg9WBwMfXrd0xpHoU3ZhizloReyLucgrFS2z2QvuYSj/0rm+nA+NYHEfeh7WZJjsyASS5fIKXilBSIVzrzsLewsmiBStt99zsRTSQLDRWgddMjsWmNQBlOBZtk/ESzGOgAeqxpaQiS6dZodv8EH1ulg7uRsi80eKZ+T4xAaj2UgZ2UYPr6tzcV//KaiekWWyMexolhIZ0v6iYCmwhPy8Adrhg1YmgJUMXtrZj2QQE1trKMLeHrp/h/UsvnPJLzrk+z5fKijjQ6REfoBHnoHJXRJaqgKqJojB7QE3p27p1H58V5nY+mnEVmH/2A8/YJOIaWOg== ⇠ | | Lüst, Palti, Vafa ‘19

• This is in contrast with some proposed AdS string vacua KKLT ’03, DeWolfe et al. ’05,… Further topics & Summary Further topics

• Further swampland conjectures and reﬁnements • Completeness in QG, moduli space conjectures, magnetic-WGC and (species) cutoffs, scalar-WGC, Stuckelberg conjectures…

• The emergence proposal and the swampland

• Phenomenological applications • Mini-charged & Fuzzy DM, natural inflation, axion monodromy and large field inflation, relaxion, cosmological constant and quintessence, massive gravity, neutrino physics, AdS/CMT…

• Swampland tests in quantum gravity and in string theory

See Palti ’19 for many more details and references The Ooguri chart The Ooguri chart (my personal take) useless useful rigorous

No global symmetry Mini-charged and Fuzzy DM Natural inflation WGC Large field inflation Distance Relaxion

AdS/CMT Neutrinos Non-SUSY AdS Hierarchy problem

Vacuum energy Inﬂation dS & AdS distance Quintessence speculative The Ooguri chart (my personal take) useless useful rigorous

No global symmetry Mini-charged and Fuzzy DM Natural inflation WGC Large field inflation Distance Relaxion

AdS/CMT Neutrinos Non-SUSY AdS Hierarchy problem

Vacuum energy Inﬂation dS & AdS distance Quintessence speculative

• Much work remains to be done to fully understand the origin and consequences of these conjectures. Stay tuned! The Ooguri chart おおきに (my personal take) useless useful rigorous

No global symmetry Mini-charged and Fuzzy DM Natural inflation WGC Large field inflation Distance Relaxion

AdS/CMT Neutrinos Non-SUSY AdS Hierarchy problem

Vacuum energy Inﬂation dS & AdS distance Quintessence speculative

• Much work remains to be done to fully understand the origin and consequences of these conjectures. Stay tuned!