The String Theory Landscape
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A String Landscape Perspective on Naturalness Outline • Preliminaries
A String Landscape Perspective on Naturalness A. Hebecker (Heidelberg) Outline • Preliminaries (I): The problem(s) and the multiverse `solution' • Preliminaries (II): From field theory to quantum gravity (String theory in 10 dimensions) • Compactifications to 4 dimensions • The (flux-) landscape • Eternal inflation, multiverse, measure problem The two hierarchy/naturalness problems • A much simplified basic lagrangian is 2 2 2 2 4 L ∼ MP R − Λ − jDHj + mhjHj − λjHj : • Assuming some simple theory with O(1) fundamental parameters at the scale E ∼ MP , we generically expectΛ and mH of that order. • For simplicity and because it is experimentally better established, I will focus in on theΛ-problem. (But almost all that follows applies to both problems!) The multiverse `solution' • It is quite possible that in the true quantum gravity theory, Λ comes out tiny as a result of an accidental cancellation. • But, we perceive that us unlikely. • By contrast, if we knew there were 10120 valid quantum gravity theories, we would be quite happy assuming that one of them has smallΛ. (As long as the calculations giving Λ are sufficiently involved to argue for Gaussian statisics of the results.) • Even better (since in principle testable): We could have one theory with 10120 solutions with differentΛ. Λ-values ! The multiverse `solution' (continued) • This `generic multiverse logic' has been advertised long before any supporting evidence from string theory existed. This goes back at least to the 80's and involves many famous names: Barrow/Tipler , Tegmark , Hawking , Hartle , Coleman , Weinberg .... • Envoking the `Anthropic Principle', [the selection of universes by demanding features which we think are necessary for intelligent life and hence for observers] it is then even possible to predict certain observables. -
String-Inspired Running Vacuum—The ``Vacuumon''—And the Swampland Criteria
universe Article String-Inspired Running Vacuum—The “Vacuumon”—And the Swampland Criteria Nick E. Mavromatos 1 , Joan Solà Peracaula 2,* and Spyros Basilakos 3,4 1 Theoretical Particle Physics and Cosmology Group, Physics Department, King’s College London, Strand, London WC2R 2LS, UK; [email protected] 2 Departament de Física Quàntica i Astrofísica, and Institute of Cosmos Sciences (ICCUB), Universitat de Barcelona, Av. Diagonal 647, E-08028 Barcelona, Catalonia, Spain 3 Academy of Athens, Research Center for Astronomy and Applied Mathematics, Soranou Efessiou 4, 11527 Athens, Greece; [email protected] 4 National Observatory of Athens, Lofos Nymfon, 11852 Athens, Greece * Correspondence: [email protected] Received: 15 October 2020; Accepted: 17 November 2020; Published: 20 November 2020 Abstract: We elaborate further on the compatibility of the “vacuumon potential” that characterises the inflationary phase of the running vacuum model (RVM) with the swampland criteria. The work is motivated by the fact that, as demonstrated recently by the authors, the RVM framework can be derived as an effective gravitational field theory stemming from underlying microscopic (critical) string theory models with gravitational anomalies, involving condensation of primordial gravitational waves. Although believed to be a classical scalar field description, not representing a fully fledged quantum field, we show here that the vacuumon potential satisfies certain swampland criteria for the relevant regime of parameters and field range. We link the criteria to the Gibbons–Hawking entropy that has been argued to characterise the RVM during the de Sitter phase. These results imply that the vacuumon may, after all, admit under certain conditions, a rôle as a quantum field during the inflationary (almost de Sitter) phase of the running vacuum. -
String Theory for Pedestrians
String Theory for Pedestrians – CERN, Jan 29-31, 2007 – B. Zwiebach, MIT This series of 3 lecture series will cover the following topics 1. Introduction. The classical theory of strings. Application: physics of cosmic strings. 2. Quantum string theory. Applications: i) Systematics of hadronic spectra ii) Quark-antiquark potential (lattice simulations) iii) AdS/CFT: the quark-gluon plasma. 3. String models of particle physics. The string theory landscape. Alternatives: Loop quantum gravity? Formulations of string theory. 1 Introduction For the last twenty years physicists have investigated String Theory rather vigorously. Despite much progress, the basic features of the theory remain a mystery. In the late 1960s, string theory attempted to describe strongly interacting particles. Along came Quantum Chromodynamics (QCD)– a theory of quarks and gluons – and despite their early promise, strings faded away. This time string theory is a credible candidate for a theory of all interactions – a unified theory of all forces and matter. Additionally, • Through the AdS/CFT correspondence, it is a valuable tool for the study of theories like QCD. • It has helped understand the origin of the Bekenstein-Hawking entropy of black holes. • Finally, it has inspired many of the scenarios for physics Beyond the Standard Model of Particle physics. 2 Greatest problem of twentieth century physics: the incompatibility of Einstein’s General Relativity and the principles of Quantum Mechanics. String theory appears to be the long-sought quantum mechanical theory of gravity and other interactions. It is almost certain that string theory is a consistent theory. It is less certain that it describes our real world. -
String Phenomenology
Introduction Model Building Moduli Stabilisation Flavour Problem String Phenomenology Joseph Conlon (Oxford University) EPS HEP Conference, Krakow July 17, 2009 Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem Chalk and Cheese? Figure: String theory and phenomenology? Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem String Theory ◮ String theory is where one is led by studying quantised relativistic strings. ◮ It encompasses lots of areas ( black holes, quantum field theory, quantum gravity, mathematics, particle physics....) and is studied by lots of different people. ◮ This talk is on string phenomenology - the part of string theory that aims at connecting to the Standard Model and its extensions. ◮ It aims to provide a (brief) overview of this area. (cf Angel Uranga’s plenary talk) Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem String Theory ◮ For technical reasons string theory is consistent in ten dimensions. ◮ Six dimensions must be compactified. ◮ Ten = (Four) + (Six) ◮ Spacetime = (M4) + Calabi-Yau Space ◮ All scales, matter, particle spectra and couplings come from the geometry of the extra dimensions. ◮ All scales, matter, particle spectra and couplings come from the geometry of the extra dimensions. Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem Model Building Various approaches in string theory to realising Standard Model-like spectra: ◮ E8 E8 heterotic string with gauge bundles × ◮ Type I string with gauge bundles ◮ IIA/IIB D-brane constructions ◮ Heterotic M-Theory ◮ M-Theory on G2 manifolds Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem Heterotic String Start with an E8 vis E8 hid gauge group in ten dimensions. -
Swampland Conjectures
Swampland Conjectures Pablo Soler - Heidelberg ITP Strings and Fields ’19 - YITP Kyoto String phenomenology & the swampland ` <latexit sha1_base64="EAxFprSVFYJYfuKS7d/uV4r6OYc=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKoMegF48RzAOSJcxOepMxszPLzKwQQv7BiwdFvPo/3vwbJ8keNLGgoajqprsrSgU31ve/vcLa+sbmVnG7tLO7t39QPjxqGpVphg2mhNLtiBoUXGLDciuwnWqkSSSwFY1uZ37rCbXhSj7YcYphQgeSx5xR66RmF4Xopb1yxa/6c5BVEuSkAjnqvfJXt69YlqC0TFBjOoGf2nBCteVM4LTUzQymlI3oADuOSpqgCSfza6fkzCl9EivtSloyV39PTGhizDiJXGdC7dAsezPxP6+T2fg6nHCZZhYlWyyKM0GsIrPXSZ9rZFaMHaFMc3crYUOqKbMuoJILIVh+eZU0L6qBXw3uLyu1mzyOIpzAKZxDAFdQgzuoQwMYPMIzvMKbp7wX7937WLQWvHzmGP7A+/wBlJiPHg==</latexit> p String/M-theory <latexit sha1_base64="8DaxENaOM20fupORTAiGRfmtnI4=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyqoMeAF48RzAOSJcxOepMxszPLzKwQQv7BiwdFvPo/3vwbJ8keNLGgoajqprsrSgU31ve/vcLa+sbmVnG7tLO7t39QPjxqGpVphg2mhNLtiBoUXGLDciuwnWqkSSSwFY1uZ37rCbXhSj7YcYphQgeSx5xR66RmF4XomV654lf9OcgqCXJSgRz1Xvmr21csS1BaJqgxncBPbTih2nImcFrqZgZTykZ0gB1HJU3QhJP5tVNy5pQ+iZV2JS2Zq78nJjQxZpxErjOhdmiWvZn4n9fJbHwTTrhMM4uSLRbFmSBWkdnrpM81MivGjlCmubuVsCHVlFkXUMmFECy/vEqaF9XArwb3V5XaZR5HEU7gFM4hgGuowR3UoQEMHuEZXuHNU96L9+59LFoLXj5zDH/gff4AlKGPEg==</latexit> `s L<latexit sha1_base64="uD+wtoefsR0DkLrUP2Tpiynljx8=">AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GNBBA8eWrAf0Iay2U7atZtN2N0IJfQXePGgiFd/kjf/jds2B219MPB4b4aZeUEiuDau++0U1tY3NreK26Wd3b39g/LhUUvHqWLYZLGIVSegGgWX2DTcCOwkCmkUCGwH45uZ335CpXksH8wkQT+iQ8lDzqixUuO+X664VXcOskq8nFQgR71f/uoNYpZGKA0TVOuu5ybGz6gynAmclnqpxoSyMR1i11JJI9R+Nj90Ss6sMiBhrGxJQ+bq74mMRlpPosB2RtSM9LI3E//zuqkJr/2MyyQ1KNliUZgKYmIy+5oMuEJmxMQSyhS3txI2oooyY7Mp2RC85ZdXSeui6rlVr3FZqd3mcRThBE7hHDy4ghrcQR2awADhGV7hzXl0Xpx352PRWnDymWP4A+fzB6RwjNM=</latexit> -
The String Theory Landscape and Cosmological Inflation
The String Theory Landscape and Cosmological Inflation Background Image: Planck Collaboration and ESA The String Theory Landscape and Cosmological Inflation Outline • Preliminaries: From Field Theory to Quantum Gravity • String theory in 10 dimensions { a \reminder" • Compactifications to 4 dimensions • The (flux-) landscape • Eternal inflation and the multiverse • Slow-roll inflation in our universe • Recent progress in inflation in string theory From Particles/Fields to Quantum Gravity • Naive picture of particle physics: • Theoretical description: Quantum Field Theory • Usually defined by an action: Z 4 µρ νσ S(Q)ED = d x Fµν Fρσ g g with T ! @Aµ @Aν 0 E Fµν = − = @xν @xµ −E "B Gravity is in principle very similar: • The metric gµν becomes a field, more precisely Z 4 p SG = d x −g R[gµν] ; where R measures the curvature of space-time • In more detail: gµν = ηµν + hµν • Now, with hµν playing the role of Aµ, we find Z 4 ρ µν SG = d x (@ρhµν)(@ h ) + ··· • Waves of hµν correspond to gravitons, just like waves of Aµ correspond to photons • Now, replace SQED with SStandard Model (that's just a minor complication....) and write S = SG + SSM : This could be our `Theory of Everything', but there are divergences .... • Divergences are a hard but solvable problem for QFT • However, these very same divergences make it very difficult to even define quantum gravity at E ∼ MPlanck String theory: `to know is to love' • String theory solves this problem in 10 dimensions: • The divergences at ~k ! 1 are now removed (cf. Timo Weigand's recent colloquium talk) • Thus, in 10 dimensions but at low energy (E 1=lstring ), we get an (essentially) unique 10d QFT: µνρ µνρ L = R[gµν] + FµνρF + HµνρH + ··· `Kaluza-Klein Compactification’ to 4 dimensions • To get the idea, let us first imagine we had a 2d theory, but need a 1d theory • We can simply consider space to have the form of a cylinder or `the surface of a rope': Image by S. -
(No) Eternal Inflation and Precision Higgs Physics
(No) Eternal Inflation and Precision Higgs Physics Nima Arkani-Hameda, Sergei Dubovskyb;c, Leonardo Senatoreb, Giovanni Villadorob aSchool of Natural Sciences, Institute for Advanced Study, Olden Lane, Princeton, NJ 08540, USA b Jefferson Physical Laboratory, Harvard University, Cambridge, MA 02138, USA c Institute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary Prospect, 7a, 117312 Moscow, Russia Abstract Even if nothing but a light Higgs is observed at the LHC, suggesting that the Standard Model is unmodified up to scales far above the weak scale, Higgs physics can yield surprises of fundamental significance for cosmology. As has long been known, the Standard Model vacuum may be metastable for low enough Higgs mass, but a specific value of the decay rate holds special significance: for a very narrow window of parameters, our Universe has not yet decayed but the current inflationary period can not be future eternal. Determining whether we are in this window requires exquisite but achievable experimental precision, with a measurement of the Higgs mass to 0.1 GeV at the LHC, the top mass to 60 MeV at a linear collider, as well as an improved determination of αs by an order of magnitude on the lattice. If the parameters are observed to lie in this special range, particle physics will establish arXiv:0801.2399v2 [hep-ph] 2 Apr 2008 that the future of our Universe is a global big crunch, without harboring pockets of eternal inflation, strongly suggesting that eternal inflation is censored by the fundamental theory. This conclusion could be drawn even more sharply if metastability with the appropriate decay rate is found in the MSSM, where the physics governing the instability can be directly probed at the TeV scale. -
Lectures on Naturalness, String Landscape and Multiverse
Lectures on Naturalness, String Landscape and Multiverse Arthur Hebecker Institute for Theoretical Physics, Heidelberg University, Philosophenweg 19, D-69120 Heidelberg, Germany 24 August, 2020 Abstract The cosmological constant and electroweak hierarchy problem have been a great inspira- tion for research. Nevertheless, the resolution of these two naturalness problems remains mysterious from the perspective of a low-energy effective field theorist. The string theory landscape and a possible string-based multiverse offer partial answers, but they are also controversial for both technical and conceptual reasons. The present lecture notes, suitable for a one-semester course or for self-study, attempt to provide a technical introduction to these subjects. They are aimed at graduate students and researchers with a solid back- ground in quantum field theory and general relativity who would like to understand the string landscape and its relation to hierarchy problems and naturalness at a reasonably technical level. Necessary basics of string theory are introduced as part of the course. This text will also benefit graduate students who are in the process of studying string theory arXiv:2008.10625v3 [hep-th] 27 Jul 2021 at a deeper level. In this case, the present notes may serve as additional reading beyond a formal string theory course. Preface This course intends to give a concise but technical introduction to `Physics Beyond the Standard Model' and early cosmology as seen from the perspective of string theory. Basics of string theory will be taught as part of the course. As a central physics theme, the two hierarchy problems (of the cosmological constant and of the electroweak scale) will be discussed in view of ideas like supersymmetry, string theory landscape, eternal inflation and multiverse. -
Introduction to String Theory A.N
Introduction to String Theory A.N. Schellekens Based on lectures given at the Radboud Universiteit, Nijmegen Last update 6 July 2016 [Word cloud by www.worldle.net] Contents 1 Current Problems in Particle Physics7 1.1 Problems of Quantum Gravity.........................9 1.2 String Diagrams................................. 11 2 Bosonic String Action 15 2.1 The Relativistic Point Particle......................... 15 2.2 The Nambu-Goto action............................ 16 2.3 The Free Boson Action............................. 16 2.4 World sheet versus Space-time......................... 18 2.5 Symmetries................................... 19 2.6 Conformal Gauge................................ 20 2.7 The Equations of Motion............................ 21 2.8 Conformal Invariance.............................. 22 3 String Spectra 24 3.1 Mode Expansion................................ 24 3.1.1 Closed Strings.............................. 24 3.1.2 Open String Boundary Conditions................... 25 3.1.3 Open String Mode Expansion..................... 26 3.1.4 Open versus Closed........................... 26 3.2 Quantization.................................. 26 3.3 Negative Norm States............................. 27 3.4 Constraints................................... 28 3.5 Mode Expansion of the Constraints...................... 28 3.6 The Virasoro Constraints............................ 29 3.7 Operator Ordering............................... 30 3.8 Commutators of Constraints.......................... 31 3.9 Computation of the Central Charge..................... -
UNIVERSITÀ DEGLI STUDI DI PADOVA Dipartimento Di Fisica E Astronomia “Galileo Galilei”
UNIVERSITÀ DEGLI STUDI DI PADOVA Dipartimento di Fisica e Astronomia “Galileo Galilei” Corso di Laurea Magistrale in Fisica Tesi di Laurea Non perturbative instabilities of Anti-de Sitter solutions to M-theory Relatore Laureanda Dr. Davide Cassani Ginevra Buratti Anno Accademico 2017/2018 Contents 1 Introduction 1 2 Motivation 7 2.1 The landscape and the swampland . .8 2.2 The Weak Gravity Conjecture . .8 2.3 Sharpening the conjecture . 11 3 False vacuum decay 15 3.1 Instantons and bounces in quantum mechanics . 16 3.2 The field theory approach . 24 3.3 Including gravity . 29 3.4 Witten’s bubble of nothing . 33 4 M-theory bubbles of nothing 37 4.1 Eleven dimensional supergravity . 38 4.2 Anti-de Sitter geometry . 41 4.3 Young’s no-go argument . 47 4.4 Re-orienting the flux . 53 4.5 M2-brane instantons . 59 5 A tri-Sasakian bubble geometry? 65 6 Conclusions 77 A Brane solutions in supergravity 79 B Anti-de Sitter from near-horizon limits 83 iii iv CONTENTS Chapter 1 Introduction There are several reasons why studying the stability properties of non supersymmetric Anti- de Sitter (AdS) spaces deserves special interest. First, AdS geometries naturally emerge in the context of string theory compactifications, here including M-theory. General stability arguments can be drawn in the presence of supersymmetry, but the question is non trivial and still open for the non supersymmetric case. However, it has been recently conjectured by Ooguri and Vafa [1] that all non supersymmetric AdS vacua supported by fluxes are actually unstable. -
Swampland, Trans-Planckian Censorship and Fine-Tuning
Swampland, Trans-Planckian Censorship and Fine-Tuning Problem for Inflation: Tunnelling Wavefunction to the Rescue Suddhasattwa Brahma1∗, Robert Brandenberger1† and Dong-han Yeom2,3‡ 1 Department of Physics, McGill University, Montr´eal, QC H3A 2T8, Canada 2 Department of Physics Education, Pusan National University, Busan 46241, Republic of Korea 3 Research Center for Dielectric and Advanced Matter Physics, Pusan National University, Busan 46241, Republic of Korea Abstract The trans-Planckian censorship conjecture implies that single-field models of inflation require an extreme fine-tuning of the initial conditions due to the very low-scale of inflation. In this work, we show how a quantum cosmological proposal – namely the tunneling wavefunction – naturally provides the necessary initial conditions without requiring such fine-tunings. More generally, we show how the tunneling wavefunction can provide suitable initial conditions for hilltop inflation models, the latter being typically preferred by the swampland constraints. 1 TCC Bounds on Inflation The trans-Planckian censorship conjecture (TCC), proposed recently [1], aims to resolve an old problem for inflationary cosmology. The idea that observable classical inhomogeneities are sourced by vacuum quantum fluctuations [2, 3] lies at the heart of the remarkable arXiv:2002.02941v2 [hep-th] 20 Feb 2020 success of inflationary predictions. On the other hand, if inflation lasted for a long time, then one can sufficiently blue-shift such macroscopic perturbations such that they end up as quantum fluctuations on trans-Planckian scales [4]. This would necessarily require the validity of inflation, as an effective field theory (EFT) on curved spacetimes, beyond the Planck scale. This is what the TCC aims to prevent by banishing any trans-Planckian mode from ever crossing the Hubble horizon and, thereby, setting an upper limit on the duration of inflation. -
String Phenomenology 1 Minimal Supersymmetric Standard Model
Swedish String/Supergravity Course 2008 String Phenomenology Marcus Berg 1 Minimal Supersymmetric Standard Model A good reference is Martin [2], a review that was first posted on hep-ph in 1997 but which has been updated three times, most recently in 2006. The MSSM consists of a number of chiral and vector supermultiplets, one for each existing quark or 1 lepton or gauge boson Aµ in the Standard Model (SM): spin: 0 1/2 1 N = 1 chiral supermultiplet φ N = 1 vector supermultiplet λ Aµ The new fields, the superpartners of and Aµ, are denoted by tildes and called "s-" for the new scalars, ~, and "-ino" for the new fermions, A~: 0 1/2 1 squarks, sleptons −! ~ − quarks, leptons gauginos−! A~ Aµ − gauge bosons This is just the generic notation; usually one is more specific. So for example, one N = 1 chiral mul- tiplet has the t quark as the fermionic field, and the scalar superpartner is the "stop", t~. We impose that the superpartner masses are around the TeV scale, or even a little lower. The scale of superpartner masses is not \derived" in any real sense2 in the MSSM, but from the point of view of particle phenomenology, an MSSM-like theory with only very heavy superpartners would be indistinguishable from the nonsuper- symmetric standard model at any experiments done in the foreseeable future, so why bother? In fact, even string theorists should have some favored scenario what will happen at near-future experiments and observations, so let's try to understand where people who do experiments for a living have put their money.