Constructing a String Theory Background Using Brane-Simplex Duality
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JHEP10(2009)051 3 3 2), | S 1 Ads , (1 × 3 Heory P SU August 10, 2009 October 20, 2009 : : September 20, 2009 : Ads Received , Published Unting in D1-D5 Systems
Published by IOP Publishing for SISSA Received: August 10, 2009 Accepted: September 20, 2009 Published: October 20, 2009 3 Asymptotic symmetries of string theory on AdS3 × S JHEP10(2009)051 with Ramond-Ramond fluxes Sujay K. Ashok,a,b Raphael Benichouc and Jan Troostc aInstitute of Mathematical Sciences, C.I.T Campus, Taramani, Chennai, 600113 India bPerimeter Institute for Theoretical Physics, Waterloo, Ontario, ON N2L2Y5, Canada cLaboratoire de Physique Th´eorique, Unit´eMixte du CRNS et de l’Ecole´ Normale Sup´erieure associ´ee `al’Universit´ePierre et Marie Curie 6, UMR 8549, 24 Rue Lhomond, Paris 75005, France E-mail: [email protected], [email protected], [email protected] Abstract: String theory on AdS3 space-times with boundary conditions that allow for black hole states has global asymptotic symmetries which include an infinite dimensional conformal algebra. Using the conformal current algebra for sigma-models on P SU(1, 1 2), | we explicitly construct the R-symmetry and Virasoro charges in the worldsheet theory describing string theory on AdS S3 with Ramond-Ramond fluxes. We also indicate how 3 × to construct the full boundary superconformal algebra. The boundary superconformal algebra plays an important role in classifying the full spectrum of string theory on AdS3 with Ramond-Ramond fluxes, and in the microscopic entropy counting in D1-D5 systems. Keywords: AdS-CFT Correspondence, Conformal Field Models in String Theory ArXiv ePrint: 0907.1242 c SISSA 2009 doi:10.1088/1126-6708/2009/10/051 Contents 1 Introduction 1 3 -
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. -
Exercise 3 — Supersymmetry for Superstrings
Arash Ardehali String Theory | Prof. Sheikh-Jabbari Exercise 3 | Supersymmetry for Superstrings 1. SUSY generalities (suggested reading : Vafa et. al., Mirror symmetry, Ch 10) Supersymmetry often leads to: I) stability of quantum systems, and II) control over the non-perturbative regime of quantum systems. As for item I, in string theory supersymmetry allows removing the bosonic string tachyon in Minkowski background. (Question: do you remember the masses of the open and closed bosonic string tachyons in Minkowski background?) In other words, the superstring spectrum, unlike the bosonic spectrum, does not signal a perturbative instability in the system. The fact that supersymmetry (SUSY) removes the tachyon (after GSO, of course), is in accord with the general wisdom that supersymmetry often stabilizes quantum systems. • Write down the N = (1; 1) SUSY algebra (in terms of Hilbert-space operators) in 1+0, 1+1, and 1+3 dimensional quantum field theories. [Hint: ask Google.] Make sure you understand the role of y. Show that in all cases the SUSY algebra implies a positive semi-definite energy. [Hint: write the expectation value of the Hamiltonian in terms of the supercharge operators.] • Write down the SUSY algebra in 1+1 dimensional conformal field theory (CFT). This CFT could be the one living on the worldsheet of superstrings. Does the algebra imply a positivity constraint on the spectrum? Task: read about Witten's SUSY-inspired proof of the positive energy theorem in clas- sical GR. As for item II, in string theory supersymmetry allows understanding various strong- weak dualities between the five superstring theories and M-theory. -
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> -
Modular Constraints on Superconformal Field Theories
KIAS-P18096 Modular Constraints on Superconformal Field Theories Jin-Beom Bae, Sungjay Lee, and Jaewon Song Korea Institute for Advanced Study 85 Hoegiro, Dongdaemun-Gu, Seoul 02455, Korea Abstract We constrain the spectrum of N = (1; 1) and N = (2; 2) superconformal field theories in two-dimensions by requiring the NS-NS sector partition function to be invariant under the Γθ congruence subgroup of the full modular group SL(2; Z). We employ semi-definite programming to find constraints on the allowed spectrum of operators with or without U(1) charges. Especially, the arXiv:1811.00976v1 [hep-th] 2 Nov 2018 upper bounds on the twist gap for the non-current primaries exhibit interest- ing peaks, kinks, and plateau. We identify a number of candidate rational (S)CFTs realized at the numerical boundaries and find that they are realized as the solutions to modular differential equations associated to Γθ. Some of the candidate theories have been discussed by H¨ohnin the context of self-dual ex- tremal vertex operator (super)algebra. We also obtain bounds for the charged operators and study their implications to the weak gravity conjecture in AdS3. Contents 1 Introduction 1 2 Preliminaries 7 2.1 Representations of N = 1 Superconformal Algebra . .7 2.2 Representations of N = 2 Superconformal Algebra . .9 2.3 Semi-Definite Programming . 12 3 Charge Independent Bounds 14 3.1 Spin-independent bounds on the gap . 14 3.2 Spin-dependent Bounds for N = (1; 1) SCFT . 16 3.3 Spin-dependent Bounds for N = (2; 2) SCFT . 26 4 Charge Dependent Bounds 29 4.1 HFK-type Bound for the Charged States . -
(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. -
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. -
Comments on String Theory on Adss
© 1998 International Press Adv. Theor. Math. Phys. 2 (1998) 733-782 Comments on String Theory on AdSs Amit Giveona, David Kutasovb, Nathan Seibergc aRacah Institute of Physics The Hebrew University Jerusalem 91904, Israel b Department of Physics University of Chicago 5640 S. Ellis Av. Chicago, IL 60637, USA ^Department of Physics of Elementary Particles Weizmann Institute of Science Rehovot, Israel cSchool of Natural Sciences Institute for Advanced Study Olden Lane Princeton, NJ, USA Abstract We study string propagation on AdSs times a compact space from an "old fashioned" worldsheet point of view of perturbative string theory. We derive the spacetime CFT and its Virasoro and current algebras, thus establishing the conjectured AdS/CFT correspondence for this case in the full string theory. Our results have implications for the extreme IR limit of the Dl - D5 system, as well as to 2+1 dimensional BTZ black holes and their Bekenstein-Hawking entropy. e-print archive: http://xxx.lanl.gov/abs/hep-th/9806194 734 COMMENTS ON STRING THEORY ON AdSz 1 Introduction The purpose of this paper is to study string propagation on curved spacetime manifolds that include AdS^. We will mostly discuss the Euclidean version also known as H^ = 51/(2, C)/SU(2) (in Appendix A we will comment on the Lorentzian signature version of AdS^, which is the SX(2, R) group man- ifold) . At low energies the theory reduces to 2 + 1 dimensional gravity with a negative cosmological constant coupled (in general) to a large collection of matter fields. The low energy action is but we will go beyond this low energy approximation. -
String Theory 101 Lectures at the International School of Strings and Fundamental Physics
String Theory 101 Lectures at the International School of Strings and Fundamental Physics Munich July 26 - August 6 2010 Neil Lambert Theory Division CERN 1211 Geneva 23 Switzerland Email: [email protected] 1 Contents 1 Introduction: Why String Theory? 3 2 Classical and Quantum Dynamics of Point Particles 4 2.1 Classical Action . 4 2.2 Electromagnetic field . 7 2.3 Quantization . 8 3 Classical and Quantum Dynamics of Strings 10 3.1 Classical Action . 10 3.2 Spacetime Symmetries and Conserved Charges . 13 3.3 Quantization . 14 3.4 Open Strings . 23 3.5 Closed Strings . 27 4 Light-cone gauge 31 4.1 D = 26, a =1................................. 33 4.2 Partition Function . 34 5 Curved Spacetime and an Effective Action 36 5.1 Strings in Curved Spacetime . 36 5.2 A Spacetime Effective Action . 38 6 Superstrings 39 6.1 Type II strings . 39 6.2 Type I and Heterotic String . 44 6.3 The Spacetime Effective Action . 46 2 1 Introduction: Why String Theory? The so-called Standard Model of Particle Physics is the most successful scientific theory of Nature in the sense that no other theory has such a high level of accuracy over such a complete range of physical phenomena using such a modest number of assumptions and parameters. It is unreasonably good and was never intended to be so successful. Since its formulation around 1970 there has not been a single experimental result that has produced even the slightest disagreement. Nothing, despite an enormous amount of effort. But there are skeletons in the closet. -
Matthew Reece Harvard University
Exploring the Weak Gravity Conjecture Matthew Reece Harvard University Based on 1506.03447, 1509.06374, 1605.05311, 1606.08437 with Ben Heidenreich and Tom Rudelius. & 161n.nnnnn with Grant Remmen, Thomas Roxlo, and Tom Rudelius Ooguri, Vafa 2005 Concretely: How good can approximate symmetries be? Can an approx. global symmetry be “too good to be true” and put a theory in the swampland? Approximate Symmetries For large-field, natural inflation we might like to have a good approximate shift symmetry φ φ + f, f > M ! Pl In effective field theory, nothing is wrong with this. In quantum gravity, it is dangerous. Quantum gravity theories have no continuous global symmetries. Basic reason: throw charged stuff into a black hole. No hair, so it continues to evaporate down to the smallest sizes we trust GR for. True of arbitrarily large charge ⇒ violate entropy bounds. (see Banks, Seiberg 1011.5120 and references therein) The Power of Shift Symmetries Scalar fields with good approximate shift symmetries can play a role in: • driving expansion of the universe (now or in the past) • solving the strong CP problem • making up the dark matter • breaking supersymmetry • solving cosmological gravitino problems These are serious, real-world phenomenological questions! Example: QCD Axion Weinberg/Wilczek/…. taught us to promote theta to field: a ↵s µ⌫ Gµ⌫ G˜ instantons: shift-symmetric potential fa 8⇡ di Cortona et al. 1511.02867 Important point: large field range, small spurion 2 2 2 2 2 1 m f (md/mu) 1 m f (md/mu)((md/mu) (md/mu) + 1) 2 ⇡ ⇡ λ = ⇡ ⇡ − ma = 2 2 4 4 f (1 + (md/mu)) −f (1 + md/mu) Example: QCD Axion 9 • Stellar cooling constraints: fa >~ 10 GeV • This means the quartic coupling <~ 10-41. -
Swampland Constraints on 5D N = 1 Supergravity Arxiv:2004.14401V2
Prepared for submission to JHEP Swampland Constraints on 5d N = 1 Supergravity Sheldon Katz, a Hee-Cheol Kim, b;c Houri-Christina Tarazi, d Cumrun Vafa d aDepartment of Mathematics, MC-382, University of Illinois at Urbana-Champaign, Ur- bana, IL 61801, USA bDepartment of Physics, POSTECH, Pohang 790-784, Korea cAsia Pacific Center for Theoretical Physics, Postech, Pohang 37673, Korea dDepartment of Physics, Harvard University, Cambridge, MA 02138, USA Abstract: We propose Swampland constraints on consistent 5-dimensional N = 1 supergravity theories. We focus on a special class of BPS magnetic monopole strings which arise in gravitational theories. The central charges and the levels of current algebras of 2d CFTs on these strings can be calculated by anomaly inflow mechanism and used to provide constraints on the low-energy particle spectrum and the effective action of the 5d supergravity based on unitarity of the worldsheet CFT. In M-theory, where these theories are realized by compactification on Calabi-Yau 3-folds, the spe- cial monopole strings arise from wrapped M5-branes on special (\semi-ample") 4- cycles in the threefold. We identify various necessary geometric conditions for such cycles to lead to requisite BPS strings and translate these into constraints on the low-energy theories of gravity. These and other geometric conditions, some of which can be related to unitarity constraints on the monopole worldsheet, are additional arXiv:2004.14401v2 [hep-th] 13 Jul 2020 candidates for Swampland constraints on 5-dimensional N = 1 supergravity