DOCSLIB.ORG

A Brief Introduction to the Weak Gravity Conjecture Eran Palti Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
A Brief Introduction to the Weak Gravity Conjecture Eran Palti Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel Letters in High Energy Physics LHEP-176, 2020 A Brief Introduction to the Weak Gravity Conjecture Eran Palti Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel Abstract The Weak Gravity Conjecture proposes that a theory with a gauge field that is coupled to gravity must have charged matter on which gravity acts as the weakest force. It also proposes that there is an intrinsic cutoff on such an effective theory, which corresponds to a tower of charged states, that is set by the strength of the gauge coupling (in Planck units). This article is a brief introduction to the Weak Gravity Conjecture, covering aspects of the motivations for it as well as various extensions and refinements. Keywords: Swampland, Quantum Gravity, String Theory gauge fields for simplicity), with gauge coupling g, there must DOI: 10.31526/LHEP.2020.176 exist at least one particle with quantized charge q and mass m which satisfies the bound p 1. INTRODUCTION m ≤ 2gqMp . (4) There are four known forces in the universe: the strong and The bound (4) is termed the Electric WGC. This is to dif- weak forces, electromagnetism, and gravity. The known fun- ferentiate it from a related bound termed the Magnetic WGC. damental matter particles are all charged under at least two The simplest way to introduce this second bound is through the of these forces. For example, the right-handed electron carries electromagnetic dual of (4) [1]. Under electromagnetic duality electromagnetic charge and gravitational charge. These charges the gauge coupling g is exchanged for its inverse g−1, while the can be deduced from the Coulomb forces that two electrons feel electrically charged particle is exchanged for a monopole with when placed a distance r apart. There is a gravitational attrac- mass mMon. So we have tive force !2 p 1 m = p e 2 FGrav 2 , (1) mMon ≤ Mp , (5) 4pr 2Mp g where me is the electron mass, and Mp is the Planck mass. And where the electric charge is taken to be one for simplicity. The there is the electromagnetic repulsive Coulomb force mass of a monopole is at least the energy stored in its magnetic field. This is infinite unless we place a cutoff L on the effective 1 2 F = (g qe) . (2) theory where the description of the monopole as a particle must EM 4pr2 EM break down. This cutoff is related to the mass of the monopole Here the electric charge is gEMqe which we have chosen to split through L into a continuous parameter gEM which sets the strength of the ∼ mMon 2 . (6) electromagentic force, and a quantized charge qe associated to g the electron in particular (that is conventionally taken to be one Combining (5) and (6) we obtain the Magnetic WGC qe = 1). The numerical values of the charges are gM me −22 −1 L . p . (7) p ∼ 10 , gEMqe ∼ 10 . (3) 2M p What is the meaning of the cutoff L? What type of new The electromagnetic force acts roughly 21 orders of magnitude physics must appear there? One way to approach this ques- more strongly on the electron than gravity. We can say that of tion is to consider how the Electric WGC (4) must behave un- all the forces which act on the electron, gravity is the weakest der renormalization. First, since the gauge coupling and mass one.1 both run with energy scale, we should determine at which en- So in our universe there exists at least one particle on which ergy scale should (4) be expected to hold. To violate the bound, gravity acts as the weakest force. Could it have been any differ- we need to show that there is no charged particle in the theory ent? The Weak Gravity Conjecture (WGC) states that it could up to the mass scale ∼ gMp. Therefore, the bound should be not have been [1]. Roughly speaking, it postulates that in any evaluated at that scale. Consider the case where the WGC par- 2 consistent theory of physics which includes gravity, there must ticle satisfying the bound (4) is a scalar. The mass of a scalar exist at least one particle on which gravity acts as the weak- runs naturally to the cutoff scale of the theory L. However, the est force. Importantly, this does not mean that it is the weakest gauge coupling, being a technically natural parameter, is only force acting on all particles. If we convert this statement into logarithmically sensitive to the cutoff. The bound (4) therefore parameters which appear in the Lagrangian, we have the state- only makes sense from a radiative naturalness perspective if ment that in a theory with a gauge field (let us restrict to U(1) (7) is satisfied. What if we want to keep the bound (4) above 1Note that there are forces in nature which act on the electron even more 2The case of a fermion follows the same logic by relating the mass of the weakly, for example the strong force, but this is because the electron is completely fermion to the expectation value of a Higgs field through (technically natural) uncharged under them and so they have exactly zero action. Yukawa couplings. 1 Letters in High Energy Physics LHEP-176, 2020 the scale gMp? Then we should require that the gauge coupling exist an appropriately charged particle. It is simple to show that begins to run with energy scale as a power-law rather than log- the requirement on that charge is exactly the Electric WGC [1]. arithmically above the scale L. The only way to do this is that a However, it remains an open problem to show that something tower of charged particles should appear at that scale. Integrat- goes wrong in a theory where black holes cannot discharge. ing in such a tower leads to the required power-law running One approach is that if black holes cannot discharge, then of the gauge coupling. This is one motivation for a refined ver- after shedding their mass through Hawking radiation, they will sion of the Magnetic WGC which states that the scale L in (7) is lead to remnants which are stable due to the charge, and that actually the mass scale of an infinite tower of charged particles such remnants may violate some principles of quantum grav- of increasing masses and charges (such that at each level (4) is ity such as entropy bounds. However, black holes satisfy an satisfied) [2, 3, 4, 5, 6, 7]. So we have extremality bound p m¥ ∼ gMp , (8) MBH ≥ 2gQBH Mp , (9) with m¥ denoting the mass scale of an infinite tower of par- where MBH is the black hole mass, and QBH its quantized ticles, so the particle of quantized charge n would have mass charge. The bound means that any remnant mass is bounded 3 n m¥. from below by its charge, and so at finite gauge coupling only a finite number Nrem of remnants can exist below the Planck −1 scale, Nrem ∼ g . It is reasonable that an infinite number of 2. QUANTUM GRAVITY AND THE WGC remnants below a finite mass scale is an inconsistent situation, but this only occurs in the g ! 0 limit. Such a limit is censored The Weak Gravity Conjecture is part of the more general through the Magnetic WGC since an infinite tower of states Swampland program which aims at determining constraints becomes massless. Indeed, far from forbidding stable charged on effective theories that are requirements for them to poten- particles below Mp, the Magnetic WGC requires them. From tially have an ultraviolet completion. See [8] for a comprehen- this perspective, the absence of black hole discharge processes sive review. The Swampland constraints are associated to the does not appear problematic. presence of gravity and so with the existence of an ultraviolet Do a finite number of remnants N violate entropy completion which includes quantum gravity. The WGC there- rem bounds? One way to approach the question is to ask if having a fore is postulated to have its origin in quantum gravity physics. number of species of particles N violates entropy bounds. This What aspects of quantum gravity could require the Electric is a question that has been studied many times (see the review (4) and Magnetic (7) constraints to hold? The primary piece of [8] for reference). In [8, 19, 20], it was proposed that the natural evidence is that they appear to hold in String Theory. Since this way to understand how N species are consistent with entropy is a brief introduction, we will not discuss the details of this, bounds is through the so-called species scale and instead refer to the review [8]. Moving away from string theory evidence, there have been Mp Ls ∼ p . (10) various proposals for general quantum gravity reasons for sup- N porting the WGC. At this point it is worthwhile distinguish- ing between two versions of the Electric WGC. The first, weak This is proposed to be the scale at which gravity becomes version, is that there is some state in the theory satisfying the strongly coupled in the presence of N species of particles. To bound (4) but this state need not be a particle. So its mass can see the relation to entropy, consider N species of weakly inter- be much larger than the Planck mass and it is best regarded as acting fields at temperature T in a box of size R. The energy a Black Hole. An extremal charged black hole will saturate (4) of the configuration scales as E ∼ NR3T4, while the entropy classically at the two-derivative level.
Load more

Recommended publications
  • Evidence for a Sublattice Weak Gravity Conjecture
    Evidence for a Sublattice Weak Gravity Conjecture The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Heidenreich, Ben, Matthew Reece, and Tom Rudelius. 2017. Evidence for a Sublattice Weak Gravity Conjecture. Journal of High Energy Physics 2017, 25. Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:41392811 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#OAP Prepared for submission to JHEP Evidence for a Sublattice Weak Gravity Conjecture Ben Heidenreich,a;b Matthew Reece,a and Tom Rudeliusa aDepartment of Physics, Harvard University, Cambridge, MA 02138, USA bPerimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5 E-mail: [email protected], [email protected], [email protected] Abstract: The Weak Gravity Conjecture postulates the existence of superextremal charged particles, i.e. those with mass smaller than or equal to their charge in Planck units. We present further evidence for our recent observation that in known examples a much stronger statement is true: an infinite tower of superextremal particles of different charges exists. We show that effective Kaluza-Klein field theories and perturbative string vacua respect the Sublattice Weak Gravity Conjecture, namely that a finite index sublattice of the full charge lattice exists with a superextremal particle at each site. In perturbative string theory we show that this follows from modular invariance.
    [Show full text]
  • Antipodal Correlation on the Meron Wormhole and a Bang-Crunch Universe
    PHYSICAL REVIEW D 97, 126006 (2018) Antipodal correlation on the meron wormhole and a bang-crunch universe Panagiotis Betzios* Crete Center for Theoretical Physics, Institute for Theoretical and Computational Physics, Department of Physics, University of Crete, 71003 Heraklion, Greece † Nava Gaddam Institute for Theoretical Physics and Center for Extreme Matter and Emergent Phenomena, Utrecht University, 3508 TD Utrecht, Netherlands ‡ Olga Papadoulaki Mathematical Sciences and STAG Research Centre, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom (Received 13 January 2018; published 11 June 2018) We present a covariant Euclidean wormhole solution to Einstein Yang-Mills system and study scalar perturbations analytically. The fluctuation operator has a positive definite spectrum. We compute the Euclidean Green’s function, which displays maximal antipodal correlation on the smallest three sphere at the center of the throat. Upon analytic continuation, it corresponds to the Feynman propagator on a compact bang-crunch universe. We present the connection matrix that relates past and future modes. We thoroughly discuss the physical implications of the antipodal map in both the Euclidean and Lorentzian geometries and give arguments on how to assign a physical probability to such solutions. DOI: 10.1103/PhysRevD.97.126006 I. INTRODUCTION whose few proposed resolutions suffer from closed time- like curves and other intricacies [10]. Euclidean wormholes [1–3] are extrema of the Euclidean Inspired by these questions, we
    [Show full text]
  • Pdf/10.1002/Andp.19053221004]
    This electronic thesis or dissertation has been downloaded from the King’s Research Portal at https://kclpure.kcl.ac.uk/portal/ Numerical general relativity and beyond formation of relativistic axion stars, boosting and colliding oscillotons, and gravitational collapse in khronometric theory Widdicombe, James Awarding institution: King's College London The copyright of this thesis rests with the author and no quotation from it or information derived from it may be published without proper acknowledgement. END USER LICENCE AGREEMENT Unless another licence is stated on the immediately following page this work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International licence. https://creativecommons.org/licenses/by-nc-nd/4.0/ You are free to copy, distribute and transmit the work Under the following conditions: Attribution: You must attribute the work in the manner specified by the author (but not in any way that suggests that they endorse you or your use of the work). Non Commercial: You may not use this work for commercial purposes. No Derivative Works - You may not alter, transform, or build upon this work. Any of these conditions can be waived if you receive permission from the author. Your fair dealings and other rights are in no way affected by the above. Take down policy If you believe that this document breaches copyright please contact [email protected] providing details, and we will remove access to the work immediately and investigate your claim. Download date: 24. Apr. 2021 Numerical General Relativity and Beyond Formation of Relativistic Axion Stars, Boosting and Colliding Oscillotons, and Gravitational Collapse in Khronometric Theory James Young Widdicombe Supervisor: Dr Eugene Lim Department of Physics King's College London A thesis presented for the degree of Doctor of Philosophy September 2019 Declaration I declare that this thesis has been composed solely by myself and that it has not been submitted, in whole or in part, in any previous application for a degree.
    [Show full text]
  • The Weak Gravity Conjecture the Weak Gravity Conjecture
    The Weak Gravity Conjecture The Weak Gravity Conjecture Arkani-Hamed et al. ‘06 • The conjecture: “Gravity is the Weakest Force” • For every long range gauge field there exists a particle of charge q and mass m, s.t. q M “1” m P ≥ M 1 P ⌘ The Weak Gravity Conjecture • Take a U(1) and a single family with q < m ( WGC ) F F F F e + g g + e M 1 P ⌘ The Weak Gravity Conjecture • Take a U(1) and a single family with q < m ( WGC ) F F F F e + g g + e BH • Form bound states Extremal ... ... BH 2m>M > 2q 3m>M3 > 3q Nm > MN >Nq M Q 2 1 ! 1 • All these (BH) states are stable. Trouble w/ remnants Susskind ‘95 M 1 P ⌘ The Weak Gravity Conjecture • Take a U(1) and a single family with q < m ( WGC ) F F F F e + g g + e BH • Form bound states Extremal ... ... BH 2m>M > 2q 3m>M3 > 3q Nm > MN >Nq M Q 2 1 ! 1 • All these (BH) states are stable. Trouble w/ remnants Susskind ‘95 • Need a light state into which they can decay q Q “1” Ext m ≥ ⌘ MExt The Weak Gravity Conjecture Arkani-Hamed et al. ‘06 • For bound states to decay, there must ∃ a particle w/ q QExt where QL is 22-dimensional vector and QR is 6-dimensional“1” vector. The charges are quan- tized, lying on the 28-dimensional even self-dualm lattice≥ with ⌘ MExt Q2 Q2 2 (21) Strong-WGC:L −satisfiedR ∈ by lightest charged particle Moving around in moduli space corresponds to making SO(22, 6) Lorentz transformations on the charges.
    [Show full text]
  • Warping the Weak Gravity Conjecture
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by University of Liverpool Repository Warping the Weak Gravity Conjecture Karta Kooner,1, ∗ Susha Parameswaran,2, y and Ivonne Zavala1, z 1Department of Physics, Swansea University, Singleton Park, Swansea, SA2 8PP, UK 2Department of Mathematical Sciences, University of Liverpool, Mathematical Sciences Building Liverpool, L69 7ZL, UK The Weak Gravity Conjecture, if valid, rules out simple models of Natural Inflation by restricting their axion decay constant to be sub-Planckian. We revisit stringy attempts to realise Natural Inflation, with a single open string axionic inflaton from a probe D-brane in a warped throat. We show that warped geometries can allow the requisite super-Planckian axion decay constant to be achieved, within the supergravity approximation and consistently with the Weak Gravity Conjecture. Preliminary estimates of the brane backreaction suggest that the probe approximation may be under control. However, there is a tension between large axion decay constant and high string scale, where the requisite high string scale is difficult to achieve in all attempts to realise large field inflation using perturbative string theory. We comment on the Generalized Weak Gravity Conjecture in the light of our results. Keywords: String theory, cosmology, inflation, D-branes, warped geometries, large axion decay constants. I. INTRODUCTION to invoke a shift symmetry in the inflaton field, for in- stance by identifying the inflaton with a Goldstone boson, Cosmological inflation stands strong as the leading the axion. The classical example in this vein is Natural mechanism to provide the seeds that gave rise to the large Inflation [5], now tightly constrained by the latest CMB 1 structure we observe today in the Universe.
    [Show full text]
  • The Weak Gravity Conjecture and Emergence from an Ultraviolet Cutoff
    Eur. Phys. J. C (2018) 78:337 https://doi.org/10.1140/epjc/s10052-018-5811-3 Regular Article - Theoretical Physics The Weak Gravity Conjecture and emergence from an ultraviolet cutoff Ben Heidenreich1,a, Matthew Reece2,b, Tom Rudelius3,c 1 Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada 2 Department of Physics, Harvard University, Cambridge, MA 02138, USA 3 School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540, USA Received: 12 March 2018 / Accepted: 16 April 2018 / Published online: 26 April 2018 © The Author(s) 2018 Abstract We study ultraviolet cutoffs associated with the ratio greater than or equal to that of a large semiclassical Weak Gravity Conjecture (WGC) and Sublattice Weak Grav- extremal black hole. ity Conjecture (sLWGC). There is a magnetic WGC cutoff at If quantum gravities exist which violate the Weak Grav- −1/2 the energy scale eGN with an associated sLWGC tower of ity Conjecture (WGC), they will have unusual properties. charged particles. A more fundamental cutoff is the scale at In particular, large near-extremal black holes in these theo- which gravity becomes strong and field theory breaks down ries cannot completely evaporate, but instead evolve slowly entirely. By clarifying the nature of the sLWGC for non- towards extremality, resulting in a tower of stable extremal abelian gauge groups we derive a parametric upper bound on black holes. However, unlike stable black hole remnants in this strong gravity scale for arbitrary gauge theories. Intrigu- theories with global symmetries, the mass of these stable ingly, we show that in theories approximately saturating the extremal black holes increases in proportion to their charge, sLWGC, the scales at which loop corrections from the tower hence the sharpest contradictions (e.g., an infinite density of charged particles to the gauge boson and graviton prop- of states in violation of the covariant entropy bound [4]) do agators become important are parametrically identical.
    [Show full text]
  • Scrambling and Decoding the Charged Quantum Information
    Scrambling and decoding the charged quantum information Junyu Liua;b aWalter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA bInstitute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA Abstract: Some deep conjectures about quantum gravity are closely related to the role of symmetries in the gravitational background, especially for quantum black holes. In this paper, we systematically study the theory of quantum information for a charged, chaotic system. We show how the quantum information in the whole system has been represented by its charge sectors, using the theory of quantum chaos and quantum error correction, with concrete examples in the context of the complex SYK model. We discuss possible implications for black hole thought experiments and conjectures about quantum gravity in the dynamical setup. We believe this work will have poten- tial applications from theories of quantum gravity to quantum simulation in quantum devices. arXiv:2003.11425v3 [quant-ph] 13 Oct 2020 Contents 1 Overview1 2 Preliminaries4 3 Chaos 13 3.1 Form factor 14 3.1.1 General result 14 3.1.2 Haar randomness 16 3.2 OTOCs 16 3.2.1 General result 16 3.2.2 Haar randomness 18 3.2.3 k-invariant subspace 19 3.3 Frame potential 21 3.3.1 General result 21 3.3.2 Haar randomness 22 3.3.3 k-invariant subspace 23 3.4 Decoupling 24 4 Example: the complex SYK model 26 5 Codes 30 5.1 Quantum error correction for the Haar randomness 31 5.2 Error correction in
    [Show full text]
  • Can the Weak Gravity Conjecture Rule out Effective Field Theories?
    Can the Weak Gravity Conjecture Rule Out Effective Field Theories? Prashant Saraswat University of Maryland and Johns Hopkins University Conference on “The Weak Gravity Conjecture and Cosmology” at IFT UAM-CSIC Based on arXiv:1412.3457 and arXiv:1604.XXXX with Anton de la Fuente and Raman Sundrum Outline • Intro: Why EFT and WGC? • Review: Forms of the WGC and bottom-up motivations • Example: Higgsing to generate violation of WGC at low energies • Extremal black hole decay? • Magnetic monopoles? • Revisiting Extranatural Inflation: Minimality + WGC makes predictions • Proposed “ultimate” WGC: Bound on cutoff is logarithmic in the gauge coupling? The Weak Gravity Conjecture and Cosmology The Weak Gravity Conjecture and Cosmology Many different claims under this name, with two basic classes of arguments: • “ Top-down”: Explore candidate QG theories (e.g. examples string theory examples or emergent gauge fields) and check that constraints are satisfied. Can’t be exhaustive, only “looking under the lamppost.” • “Bottom-up”: Argue from universal, low-energy features of theories with gauge fields + gravity: charged black holes The Weak Gravity Conjecture and Cosmology Many open questions about the role of new physics to explain: • Inflation / Primordial density fluctuations • Dark matter • Dark energy (dynamical?) • Hierarchy problem (“cosmological relaxation”) Effective Field Theory The conventional wisdom: “You don’t need to know atomic physics to cook spaghetti” Effective Field Theory The conventional wisdom: describe low-energy quantum gravity physics “You don’t need to know atomic physics to cook spaghetti” Effective Field Theory The conventional wisdom: describe low-energy quantum gravity physics “You don’t need to know atomic physics to cook spaghetti” EFT: Describe systems at low energy, with UV effects suppressed by decoupling and/or symmetry.
    [Show full text]
  • Matters of Gravity, the Newsletter of the Division of Gravitational Physics of the American Physical Society, Volume 50, December 2017
    MATTERS OF GRAVITY The newsletter of the Division of Gravitational Physics of the American Physical Society Number 50 December 2017 Contents DGRAV News: we hear that . , by David Garfinkle ..................... 3 APS April Meeting, by David Garfinkle ................... 4 Town Hall Meeting, by Emanuele Berti ................... 7 Conference Reports: Hawking Conference, by Harvey Reall and Paul Shellard .......... 8 Benasque workshop 2017, by Mukund Rangamani .............. 10 QIQG 3, by Matt Headrick and Rob Myers ................. 12 arXiv:1712.09422v1 [gr-qc] 26 Dec 2017 Obituary: Remembering Cecile DeWitt-Morette, by Pierre Cartier ........... 15 Editor David Garfinkle Department of Physics Oakland University Rochester, MI 48309 Phone: (248) 370-3411 Internet: garfinkl-at-oakland.edu WWW: http://www.oakland.edu/physics/Faculty/david-garfinkle Associate Editor Greg Comer Department of Physics and Center for Fluids at All Scales, St. Louis University, St. Louis, MO 63103 Phone: (314) 977-8432 Internet: comergl-at-slu.edu WWW: http://www.slu.edu/arts-and-sciences/physics/faculty/comer-greg.php ISSN: 1527-3431 DISCLAIMER: The opinions expressed in the articles of this newsletter represent the views of the authors and are not necessarily the views of APS. The articles in this newsletter are not peer reviewed. 1 Editorial The next newsletter is due June 2018. Issues 28-50 are available on the web at https://files.oakland.edu/users/garfinkl/web/mog/ All issues before number 28 are available at http://www.phys.lsu.edu/mog Any ideas for topics that should be covered by the newsletter should be emailed to me, or Greg Comer, or the relevant correspondent. Any comments/questions/complaints about the newsletter should be emailed to me.
    [Show full text]
  • Jhep11(2020)008
    Published for SISSA by Springer Received: June 24, 2020 Accepted: September 30, 2020 Published: November 4, 2020 Duality and supersymmetry constraints on the weak JHEP11(2020)008 gravity conjecture Gregory J. Loges,a Toshifumi Noumib and Gary Shiua aDepartment of Physics, University of Wisconsin-Madison, Madison, WI 53706, U.S.A. bDepartment of Physics, Kobe University, Kobe 657-8501, Japan E-mail: [email protected], [email protected], [email protected] Abstract: Positivity bounds coming from consistency of UV scattering amplitudes are not always sufficient to prove the weak gravity conjecture for theories beyond Einstein- Maxwell. Additional ingredients about the UV may be necessary to exclude those regions of parameter space which are naïvely in conflict with the predictions of the weak gravity conjecture. In this paper we explore the consequences of imposing additional symmetries inherited from the UV theory on higher-derivative operators for Einstein-Maxwell-dilaton- axion theory. Using black hole thermodynamics, for a preserved SL(2, R) symmetry we find that the weak gravity conjecture then does follow from positivity bounds. For a preserved O(d, d; R) symmetry we find a simple condition on the two Wilson coefficients which ensures the positivity of corrections to the charge-to-mass ratio and that follows from the null energy condition alone. We find that imposing supersymmetry on top of either of these symmetries gives corrections which vanish identically, as expected for BPS states. Keywords: Black Holes, Black Holes in String Theory, String Duality, Supersymmetry and Duality ArXiv ePrint: 2006.06696 Open Access, c The Authors.
    [Show full text]
  • The Weak Gravity Conjecture in Three Dimensions Arxiv:1606.08438V1
    IFT-UAM/CSIC-16-060 FTUAM-16-25 MAD-TH-16-03 The Weak Gravity Conjecture in three dimensions Miguel Montero1;2, Gary Shiu3;4, Pablo Soler3;4 1 Departamento de F´ısicaTe´orica,Facultad de Ciencias Universidad Aut´onomade Madrid, 28049 Madrid, Spain 2 Instituto de F´ısicaTe´oricaIFT-UAM/CSIC, C/ Nicol´asCabrera 13-15, Campus de Cantoblanco, 28049 Madrid, Spain 3 Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA 4 Department of Physics & Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong Abstract We study weakly coupled U(1) theories in AdS3, their associated charged BTZ solutions, and their charged spectra. We find that modular invariance of the holographic dual two-dimensional CFT and compactness of the gauge group together imply the existence of charged operators with conformal dimension significantly below arXiv:1606.08438v1 [hep-th] 27 Jun 2016 the black hole threshold. We regard this as a form of the Weak Gravity Conjecture (WGC) in three dimensions. We also explore the constraints posed by modular invariance on a particular discrete ZN symmetry which arises in our discussion. In this case, modular invari- ance does not guarantee the existence of light ZN -charged states. We also highlight the differences between our discussion and the usual heuristic arguments for the WGC based on black hole remnants. Contents 1 Introduction 2 2 The WGC in d > 3 3 3 Gravity and gauge fields in three dimensions 5 3.1 3D U(1) gauge fields & Chern-Simons terms . .6 3.2 Consequences of compactness of the gauge group .
    [Show full text]
  • A Bridge from Quantum Gravity to Particle Physics
    universe Review The Swampland Conjectures: A Bridge from Quantum Gravity to Particle Physics Mariana Graña * and Alvaro Herráez Institut de Physique Théorique, Université Paris Saclay, CEA, CNRS, Orme des Merisiers, F-91191 Gif sur Yvette, France; [email protected] * Correspondence: [email protected] Abstract: The swampland is the set of seemingly consistent low-energy effective field theories that cannot be consistently coupled to quantum gravity. In this review we cover some of the conjectural properties that effective theories should possess in order not to fall in the swampland, and we give an overview of their main applications to particle physics. The latter include predictions on neutrino masses, bounds on the cosmological constant, the electroweak and QCD scales, the photon mass, the Higgs potential and some insights about supersymmetry. Keywords: quantum gravity; low energy effective theories; particle physics 1. Introduction Recent years have seen the emergence of a new picture, or rather, a new paradigm, of quantum gravity. It has become clear that certain low energy theories that seem consistent from several points of view (such as e.g., anomaly cancellation) cannot be coupled to Citation: Graña, M.; Herráez, A. quantum gravity in a consistent way. The low-energy theories that cannot be consistently The Swampland Conjectures: coupled to gravity are said to belong to the swampland [1]. A Bridge from Quantum Gravity On the other hand, the exploration of string theory has lead to a widely accepted to Particle Physics. Universe 2021, 7, picture of the space of string vacua. It is clear that string compactifications from 10 to 273.
    [Show full text]