DOCSLIB.ORG

Gauge/Gravity Duality Applied to Condensed Matter Systems

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Gauge/Gravity Duality Applied to Condensed Matter Systems Gauge/Gravity Duality applied to Condensed Matter Systems Martin Matthias Ammon M¨unchen 2010 Gauge/Gravity Duality applied to Condensed Matter Systems Martin Matthias Ammon Dissertation an der Fakult¨at f¨ur Physik der Ludwig–Maximilians–Universit¨at M¨unchen vorgelegt von Martin Matthias Ammon aus Roth, Mittelfranken. M¨unchen, den 31. Mai 2010 This thesis is based on the author’s work partly published in [1–9] conducted from November 2007 until May 2010 at the Max-Planck-Institut f¨ur Physik (Werner- Heisenberg-Institut), M¨unchen under supervision of Priv.-Doz. Dr. Johanna Karen Erdmenger. Erstgutachter: Priv.-Doz. Dr. Johanna Karen Erdmenger Zweitgutachter: Prof. Dr. Dieter L¨ust Tag der m¨undlichen Pr¨ufung: 07. Juli 2010 Zusammenfassung In der hier vorliegenden Arbeit werden mit Hilfe der AdS/CFT-Korrespondenz Ph¨anomene stark gekoppelter quantenkritischer Systeme untersucht, wie sie beispielsweise in Syste- men der kondensierten Materie auftreten. Die AdS/CFT-Korrespondenz ist dabei eine aus der Stringtheorie hervorgegangene Dualit¨at zwischen Eich- und Gravitationstheorien, die Rechnungen in starker Kopplung auf der Eichtheorieseite in perturbative Rechnun- gen auf der Gravitationsseite ubersetzt.¨ Dabei setzt die ursprungliche,¨ von Maldacena im Jahr 1997 entwickelte Vermutung vierdimensionale, = 4 supersymmetrische Yang- N Mills-Theorie und Typ IIB-Supergravitation im funfdimensionalen¨ Anti-de Sitter-Raum in Beziehung. Diese Vermutung kann auf verschiedene Weise verallgemeinert werden. So k¨onnen auf der Eichtheorieseite Zust¨ande mit endlicher Temperatur und Dichte betrachtet werden oder Freiheitsgrade hinzugefugt¨ werden, die sich in der fundamentalen Darstellung der Eichgruppe transformieren, die sogenannten Flavor-Freiheitsgrade Diese Deformationen der Korrespondenz werden in der hier vorliegenden Arbeit verwen- det, um stark gekoppelte Systeme in der N¨ahe von quantenkritischen Punkten besser zu verstehen. Wir approximieren hierbei die Feldtheorie am quantenkritischen Punkt durch = 4 supersymmetrische Yang-Mills-Theorie. Die Ladungstr¨ager des Systems werden N durch supersymmetrische Flavor-Felder eingefuhrt.¨ Dieses Modell ist der Ausgangspunkt von vielen Uberlegungen¨ und Untersuchungen, die im Rahmen der Dissertation durch- gefuhrt¨ wurden. Beispielsweise wird in der hier vorliegenden Arbeit im Fall von zwei Flavor Feldern, die die gleiche Masse haben, ein chemisches Potential fur¨ den Isospin betrachtet und das Phasen- diagramm untersucht. Das Isospin-chemische Potential bricht hierbei den nicht-Abelschen Anteil der Flavor-Symmetrie, SU(2), auf U(1). Wird ein kritischer Wert des Isospin- chemischen Potentials uberstiegen,¨ so zeigt unsere Rechnung, dass das stark-gekoppelte System gegenuber¨ Fluktuationen instabil wird. Es bildet sich ein neuer thermodynamisch favorisierter Zustand aus. Dieser Zustand bricht die restliche U(1) Flavorsymmetrie spon- tan und kann daher als eine Supraflussigkeit¨ angesehen werden. Ist nun die U(1) geeicht, erh¨alt man auf diese Weise einen Supraleiter. Die Wechselstrom-Leitf¨ahigkeit geht in der supraleitenden Phase fur¨ kleine Frequenzen gegen Null. Die Gleichstrom-Leitf¨ahigkeit je- doch ist unendlich, wie das auch von einem Supraleiter erwartet wird. Da der Supraleiter stark gekoppelt ist, kann dieser nicht durch die BCS Theorie beschrieben werden. Des Weiteren berechnen wir auch die Fermifl¨ache in der supraleitenden Phase und beobach- ten, dass diese auf vier ausgezeichnete Punkte kollabiert. Außerdem wird eine holographische Methode zur Berechnung der Leitf¨ahigkeit des Gleich- stroms auf beliebige konstante elektrische und magnetische Felder weiterentwickelt. Hierbei wird die Leitf¨ahigkeit nicht mit Hilfe von Linearer-Antwort-Theorie beschrieben, sondern ist selbst vom elektrischen Feld abh¨angig. Schließlich wird auch ein zweites Modell fur¨ die Feldtheorie am quantenkritischen Punkt, eine Chern-Simons-Materie Theorie in (2+1)-Dimensionen, genauer untersucht. Die Chern- Simons-Materie Theorie hat dynamische Freiheitsgrade und kann als Niederenergie-Limes vi Zusammenfassung von (2+1)-dimensionalen Membranen, sogenannter M2-Branen, aufgefasst werden. Auf verschiedene Weisen werden in der vorliegenden Arbeit auf der Eichtheorieseite Ladungs- tr¨ager in Form von fundamentalen supersymmetrischen Feldern hinzugefugt¨ und die effek- tive Kopplung an die Felder der Chern-Simons-Materie bestimmt. Auf der Gravitations- seite werden dabei h¨oherdimensionale Membranen und andere nicht-perturbative Objekte, sogenannte KK-Monopole, in M-Theorie bzw. dessen Typ IIA Limes eingebettet. Insgesamt erhoffen wir uns von diesen Untersuchungen an Modelltheorien, die sowohl Berechnungen bei starker als auch bei schwacher Kopplung zulassen, neue Impulse fur¨ die Theorie der kondensierten Materie. Dabei haben wir insbesondere quantenkritische Systeme, wie beispielsweise Hochtemperatur-Supraleiter, im Blick. Contents Zusammenfassung v 1 Introduction and Overview 1 1.1 String Theory and strongly coupled systems . ....... 3 1.2 Strongly coupled condensed matter systems . ....... 4 1.3 AdS/CFTandcondensedmattersystems . ... 8 1.4 Planofthethesis................................. 13 I Foundations of AdS/CFT 15 2 The Anti-de Sitter/Conformal Field Theory Correspondence 17 2.1 Review: TheoriginofAdS/CFT . 18 2.2 Review: TheAdS/CFTDictionary . 28 2.3 Holographic renormalization for fermions . ........ 30 2.4 Review: Generalization to finite temperature . ........ 41 2.5 Review: Addingfundamentalflavor. 43 2.6 Other examples of gauge/gravity dualities . ........ 58 II Applications to Condensed Matter Systems 61 3 Response to external fields 63 3.1 Review: Linear response & retarded Green’s functions . .......... 63 3.2 Holographic Calculation: Linear response . ........ 65 3.3 Holographic calculation: Beyond linear response . .......... 75 4 Holographic Superconductors 87 4.1 Introductionandsummary . 88 4.2 Fieldtheorydescription . 90 4.3 DualGravitypicture.............................. 91 4.4 StringTheoryPicture ............................. 99 5 Fermions in AdS/CFT 103 5.1 IntroductionandSummary . 103 5.2 Worldvolume Fermions of Dp-branes . 106 5.3 EmergenceoftheFermisurface . 114 6 Non-relativistic systems: AC & DC conductivities 129 6.1 IntroductionandSummary . 129 6.2 Adding Flavor to Schr¨odinger Spacetime . .......132 viii CONTENTS 6.3 DCConductivityofProbeFlavor . 139 6.4 ACConductivityofProbeFlavor . 145 III Flavor in Chern-Simons-Matter Theories 151 7 Adding Flavor to AdS4/CF T3 153 7.1 Introductionandsummary . 154 7.2 AM-theoryPrimer................................156 7.3 ReviewofABJMTheory ............................159 7.4 General Analysis of Probe Flavor . 163 7.5 Codimension Zero =3SupersymmetricFlavor . 169 N 7.6 Codimension One = (0, 6) Supersymmetric Flavor . 173 N 7.7 SU(4)EquivalenceofProbeFlavor . .176 7.8 Other Flavor branes in AdS4/CF T3 ......................179 8 Conclusions and Outlook 181 A Glossary 189 A.1 BosonicStringTheory . .. .. .. .. .. .. .. .. 189 A.2 SuperstringTheory............................... 197 A.3 D-branes......................................205 B Appendix to Chapter 7 211 B.1 SupersymmetryofTypeIIBProbes . 211 B.2 TypeIIBtoM-theory ..............................214 B.3 SupersymmetryofM-theoryObjects . 219 B.4 = (0, 6)SupersymmetryTransformations . 223 N Acknowledgements 240 1 Introduction and Overview In the twentieth century, physicists made much progress in the theoretical understanding of many phenomena in nature, related to quantum theory and gravity. The basic build- ing blocks of the physical world are particles and their interactions. Today, four basic interactions are known: the electromagnetic force, gravity, the weak and strong nuclear forces. Except gravity, the remaining three interactions, as well as the matter fields, can be formulated in terms of a quantum field theory, known as the standard model of particle physics. Up to now, the standard model of particle physics has been very well tested at least up to energies of 100 GeV. Every high energy physics experiment has yielded results consistent with the Standard Model. All quantized forces, which are incorporated in the standard model, can be described in terms of exchange particles. For example, the electromagnetic force is described by the exchange of massless spin-1 particles, called photons, which we denote as γ. The quan- tized theory of electrodynamics, Quantum Electrodynamics (QED), is very precise. The theoretical prediction for the anomalous magnetic moment of the electron, for example, agrees with the measured value up to one part in 1010. 0 The weak nuclear force is described by three exchange particles, W ± and Z . In contrast to the photon, the W ± and Z are massive spin-1 gauge bosons, and therefore the force is short-ranged. The weak force is responsible for nuclear beta decay, for example. Although the electromagnetic and weak forces seem to be very different, they can be formulated in a unified theory, called the electro-weak theory, in terms of a SU(2) U(1) gauge × Y theory. The electro-weak symmetry breaking mechanism breaks the SU(2) U(1) gauge × Y symmetry to the electromagnetic U(1)em group, leaving only the photon massless and giving mass to the W ± and Z boson. This symmetry breaking mechanism also predicts the existence of a massive scalar particle, called the Higgs boson. At colliders, such as the Large Hadron Collider (LHC) at CERN, experimentalists aim at discovering this Higgs boson. Finally, the strong nuclear force can be described by Quantum Chromodynamics (QCD),
Load more

Recommended publications
  • TASI Lectures on String Compactification, Model Building
    CERN-PH-TH/2005-205 IFT-UAM/CSIC-05-044 TASI lectures on String Compactification, Model Building, and Fluxes Angel M. Uranga TH Unit, CERN, CH-1211 Geneve 23, Switzerland Instituto de F´ısica Te´orica, C-XVI Universidad Aut´onoma de Madrid Cantoblanco, 28049 Madrid, Spain angel.uranga@cern,ch We review the construction of chiral four-dimensional compactifications of string the- ory with different systems of D-branes, including type IIA intersecting D6-branes and type IIB magnetised D-branes. Such models lead to four-dimensional theories with non-abelian gauge interactions and charged chiral fermions. We discuss the application of these techniques to building of models with spectrum as close as possible to the Stan- dard Model, and review their main phenomenological properties. We finally describe how to implement the tecniques to construct these models in flux compactifications, leading to models with realistic gauge sectors, moduli stabilization and supersymmetry breaking soft terms. Lecture 1. Model building in IIA: Intersecting brane worlds 1 Introduction String theory has the remarkable property that it provides a description of gauge and gravitational interactions in a unified framework consistently at the quantum level. It is this general feature (beyond other beautiful properties of particular string models) that makes this theory interesting as a possible candidate to unify our description of the different particles and interactions in Nature. Now if string theory is indeed realized in Nature, it should be able to lead not just to `gauge interactions' in general, but rather to gauge sectors as rich and intricate as the gauge theory we know as the Standard Model of Particle Physics.
    [Show full text]
  • Lectures on D-Branes
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server CPHT/CL-615-0698 hep-th/9806199 Lectures on D-branes Constantin P. Bachas1 Centre de Physique Th´eorique, Ecole Polytechnique 91128 Palaiseau, FRANCE [email protected] ABSTRACT This is an introduction to the physics of D-branes. Topics cov- ered include Polchinski’s original calculation, a critical assessment of some duality checks, D-brane scattering, and effective worldvol- ume actions. Based on lectures given in 1997 at the Isaac Newton Institute, Cambridge, at the Trieste Spring School on String The- ory, and at the 31rst International Symposium Ahrenshoop in Buckow. June 1998 1Address after Sept. 1: Laboratoire de Physique Th´eorique, Ecole Normale Sup´erieure, 24 rue Lhomond, 75231 Paris, FRANCE, email : [email protected] Lectures on D-branes Constantin Bachas 1 Foreword Referring in his ‘Republic’ to stereography – the study of solid forms – Plato was saying : ... for even now, neglected and curtailed as it is, not only by the many but even by professed students, who can suggest no use for it, never- theless in the face of all these obstacles it makes progress on account of its elegance, and it would not be astonishing if it were unravelled. 2 Two and a half millenia later, much of this could have been said for string theory. The subject has progressed over the years by leaps and bounds, despite periods of neglect and (understandable) criticism for lack of direct experimental in- put. To be sure, the construction and key ingredients of the theory – gravity, gauge invariance, chirality – have a firm empirical basis, yet what has often catalyzed progress is the power and elegance of the underlying ideas, which look (at least a posteriori) inevitable.
    [Show full text]
  • Pitp Lectures
    MIFPA-10-34 PiTP Lectures Katrin Becker1 Department of Physics, Texas A&M University, College Station, TX 77843, USA [email protected] Contents 1 Introduction 2 2 String duality 3 2.1 T-duality and closed bosonic strings .................... 3 2.2 T-duality and open strings ......................... 4 2.3 Buscher rules ................................ 5 3 Low-energy effective actions 5 3.1 Type II theories ............................... 5 3.1.1 Massless bosons ........................... 6 3.1.2 Charges of D-branes ........................ 7 3.1.3 T-duality for type II theories .................... 7 3.1.4 Low-energy effective actions .................... 8 3.2 M-theory ................................... 8 3.2.1 2-derivative action ......................... 8 3.2.2 8-derivative action ......................... 9 3.3 Type IIB and F-theory ........................... 9 3.4 Type I .................................... 13 3.5 SO(32) heterotic string ........................... 13 4 Compactification and moduli 14 4.1 The torus .................................. 14 4.2 Calabi-Yau 3-folds ............................. 16 5 M-theory compactified on Calabi-Yau 4-folds 17 5.1 The supersymmetric flux background ................... 18 5.2 The warp factor ............................... 18 5.3 SUSY breaking solutions .......................... 19 1 These are two lectures dealing with supersymmetry (SUSY) for branes and strings. These lectures are mainly based on ref. [1] which the reader should consult for original references and additional discussions. 1 Introduction To make contact between superstring theory and the real world we have to understand the vacua of the theory. Of particular interest for vacuum construction are, on the one hand, D-branes. These are hyper-planes on which open strings can end. On the world-volume of coincident D-branes, non-abelian gauge fields can exist.
    [Show full text]
  • Abdus Salam United Nations Educational, Scientific and Cultural XA9952968 Organization International Centre
    the IC/99/74 abdus salam united nations educational, scientific and cultural XA9952968 organization international centre international atomic energy agency for theoretical physics D = 4 YANG-MILLS CORRELATORS 5 FROM NSR STRINGS ON AdS5 x S Dimitri Polyakov 30-47 Available at: http://www.ictp.trieste.it/~pub-off IC/99/74 United Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS D = 4 YANG-MILLS CORRELATORS 5 FROM NSR STRINGS ON AdS5 x S Dimitri Polyakov^ The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy. Abstract In our previous work (hep-th/9812044) we have proposed the sigma-model action, conjectured to be the NSR analogue of superstring theory on AdS$ x S5. This sigma- model is the NSR superstring action with potential term corresponding to the exotic 5- form vertex operator (branelike state). This 5-form potential plays the role of cosmological term, effectively curving the flat space-time geometry to that of AdS$ x S5. In this paper we study this ansatz in more detail and provide the derivation of the correlators of the four- dimensional super Yang-Mills theory from the above mentioned sigma-model. In particular, we show that the correlation function of two dilaton vertex operators in such a model reproduces the well-known result for the two-point function in N = 4 four-dimensional 2 2 super Yang-Mills theory: < F (x)F (y) >~ \JLy\» • MIRAMARE - TRIESTE July 1999 E-mail: [email protected] Introduction One of the most profound questions with regard to critical superstring theory in ten dimensions is its relation to our four-dimensional world.
    [Show full text]
  • Brane Effective Actions, Kappa-Symmetry and Applications
    Living Rev. Relativity, 15, (2012), 3 LIVINGREVIEWS http://www.livingreviews.org/lrr-2012-3 in relativity Brane Effective Actions, Kappa-Symmetry and Applications Joan Sim´on School of Mathematics, The University of Edinburgh, and Maxwell Institute for Mathematical Sciences Edinburgh EH9 3JZ, U.K. email: [email protected] Accepted on 9 January 2012 Published on 27 February 2012 Abstract This is a review on brane effective actions, their symmetries and some of their applications. Its first part covers the Green{Schwarz formulation of single M- and D-brane effective actions focusing on kinematical aspects: the identification of their degrees of freedom, the importance of world volume diffeomorphisms and kappa symmetry to achieve manifest spacetime covari- ance and supersymmetry, and the explicit construction of such actions in arbitrary on-shell supergravity backgrounds. Its second part deals with applications. First, the use of kappa symmetry to determine supersymmetric world volume solitons. This includes their explicit construction in flat and curved backgrounds, their interpretation as Bogomol'nyi{Prasad–Sommerfield (BPS) states carrying (topological) charges in the supersymmetry algebra and the connection between su- persymmetry and Hamiltonian BPS bounds. When available, I emphasise the use of these solitons as constituents in microscopic models of black holes. Second, the use of probe approx- imations to infer about the non-trivial dynamics of strongly-coupled gauge theories using the anti de Sitter/conformal field theory (AdS/CFT) correspondence. This includes expectation values of Wilson loop operators, spectrum information and the general use of D-brane probes to approximate the dynamics of systems with small number of degrees of freedom interacting with larger systems allowing a dual gravitational description.
    [Show full text]
  • Holography and Compactification
    PUPT-1872 ITFA-99-14 Holography and Compactification Herman Verlinde Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 and Institute for Theoretical Physics, University of Amsterdam Valckenierstraat 65, 1018 XE Amsterdam Abstract arXiv:hep-th/9906182v1 24 Jun 1999 Following a recent suggestion by Randall and Sundrum, we consider string compactification scenarios in which a compact slice of AdS-space arises as a subspace of the compactifica- tion manifold. A specific example is provided by the type II orientifold equivalent to type I theory on (orbifolds of) T 6, upon taking into account the gravitational backreaction of the D3-branes localized inside the T 6. The conformal factor of the four-dimensional metric depends exponentially on one of the compact directions, which, via the holographic corre- spondence, becomes identified with the renormalization group scale in the uncompactified world. This set-up can be viewed as a generalization of the AdS/CFT correspondence to boundary theories that include gravitational dynamics. A striking consequence is that, in this scenario, the fundamental Planck size string and the large N QCD string appear as (two different wavefunctions of) one and the same object. 1 Introduction In string theory, when considered as a framework for unifying gravity and quantum mechan- ics, the fundamental strings are naturally thought of as Planck size objects. At much lower energies, such as the typical weak or strong interaction scales, the strings have lost all their internal structure and behave just as ordinary point-particles. The physics in this regime is therefore accurately described in terms of ordinary local quantum field theory, decoupled from the planckian realm of all string and quantum gravitational physics.
    [Show full text]
  • Introduction to Path Integral Methods in String Theory
    Introduction to path integral methods in string theory Sergio Ernesto Aguilar Guti´errez1 1Instituto de F´ısica Te´orica, Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz 271, 01140-070 S~aoPaulo, SP, Brazil∗ (Dated: November 30, 2018) Contents I. Introduction 1 II. Functional methods in bosonic string theory 2 A. Polyakov action 2 B. Symmetries 3 C. Equations of motion and boundary conditions 4 D. Polyakov path integral 6 E. BRST quantization 10 F. Representation theory 11 III. Functional methods in the RNS formalism 12 A. Superstring theory in the RNS formalism 12 B. R and NS sectors 14 C. Local symmetries of the action 16 D. Path integrals in RNS 17 References 19 I. INTRODUCTION The fundamentals of path integral methods in string theory are reviewed with emphasis in the development of the Faddeev Popov ghost that emerge from overcounting of configurations and the conditions that the string theory requires for maintaining Weyl invariance. Since the lecture is presented for a course that does not assume previous knowledge in string theory, I include an introduction to both bosonic and superstring theory (in the RNS formalism). This text begins with an introduction to bosonic string theory, we study the symmetries of the Polyakov action, we work out the canonical quantization of the theory to calculate its central charge. Later the path integral formulation is introduced with the appearance of Faddeev-Popov ghosts, we consider their canonical quantization for computing the central charge. The total central charge generates an anomaly in the Weyl invariance of the theory. The vanishing of such term has powerful implications that yield conditions related with the possible physical states and the dimensions of the theory.
    [Show full text]
  • University of Groningen Seven-Branes and Instantons In
    University of Groningen Seven-branes and instantons in type IIB supergravity Hartong, Jelle IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below. Document Version Publisher's PDF, also known as Version of record Publication date: 2008 Link to publication in University of Groningen/UMCG research database Citation for published version (APA): Hartong, J. (2008). Seven-branes and instantons in type IIB supergravity. s.n. Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons). Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Download date: 27-09-2021 Introduction The subject of this thesis will be introduced. The studies performed in the coming chapters attempt to improve on the understanding of certain aspects of string theory. Here, I will give a personal point of view on the subject of string theory after which I will briefly sketch the most elementary properties of string theory that allow me to further introduce the subject of this thesis.
    [Show full text]
  • Introduction to Superstring Theory
    Introduction to Superstring Theory Carmen N´u~nez IAFE (UBA-CONICET) & PHYSICS DEPT. (University of Buenos Aires) VI ICTP LASS 2015 Mexico, 26 October- 6 November 2015 . Programme Class 1: The classical fermionic string Class 2: The quantized fermionic string Class 3: Partition Function Class 4: Interactions . Outline Class 1: The classical fermionic string The action and its symmetries Gauge fixing and constraints Equations of motion and boundary conditions Oscillator expansions . The spectra of bosonic strings contain a tachyon ! it might indicate the vacuum has been incorrectly identified. The mass squared of a particle T is the quadratic term in the 2 @2V (T ) j − 4 ) action: M = @T 2 T =0 = α0 = we are expanding around a maximum of V . If there is some other stable vacuum, this is not an actual inconsistency. Why superstrings? . The mass squared of a particle T is the quadratic term in the 2 @2V (T ) j − 4 ) action: M = @T 2 T =0 = α0 = we are expanding around a maximum of V . If there is some other stable vacuum, this is not an actual inconsistency. Why superstrings? The spectra of bosonic strings contain a tachyon ! it might indicate the vacuum has been incorrectly identified. If there is some other stable vacuum, this is not an actual inconsistency. Why superstrings? The spectra of bosonic strings contain a tachyon ! it might indicate the vacuum has been incorrectly identified. The mass squared of a particle T is the quadratic term in the 2 @2V (T ) j − 4 ) action: M = @T 2 T =0 = α0 = we are expanding around a maximum of V .
    [Show full text]
  • Non-Supersymmetric Ads and the Swampland
    CALT-TH 2016-027, IPMU16-0139 Non-supersymmetric AdS and the Swampland Hirosi Ooguria,b and Cumrun Vafac a Walter Burke Institute for Theoretical Physics California Institute of Technology, Pasadena, CA 91125, USA b Kavli Institute for the Physics and Mathematics of the Universe University of Tokyo, Kashiwa, 277-8583, Japan c Center for the Fundamental Laws of Nature Harvard University, Cambridge, MA 02138, USA Abstract We propose to sharpen the weak gravity conjecture by the statement that, except for BPS states in a supersymmetric theory, the gravitational force is strictly weaker than any electric force and provide a number of evidences for this statement. Our conjecture implies that any non-supersymmetric anti-de Sitter vacuum supported by fluxes must be unstable, as is the case for all known attempts at such holographic constructions. arXiv:1610.01533v3 [hep-th] 25 Aug 2017 1 Introduction The weak gravity conjecture (WGC) [1] is an example of how seemingly consistent low energy gravitational theories can fail to have ultra-violet completion and instead belong to the swampland [2]; see [3] for more swampland constraints. Recently, there have been a number of papers checking and extending the WGC and applying it to cosmology [4–7,9–12]. The conjecture has also been related to the holographic principle in [13]. In this brief note, we propose sharpening of the WGC and point out that it implies that non-supersymmetric anti-de Sitter (AdS) vacua supported by fluxes are unstable. The WGC states that the mass of a particle carrying a basic unit of charge or its small multiple is less than or equal to that predicted if the particle were an extremal black hole.
    [Show full text]
  • Lecture 1. Model Building in IIA: Intersecting Brane Worlds
    Compactification, Model Building, and Fluxes Angel M. Uranga IFT, Madrid, and CERN, Geneva Lecture 1. Model building in IIA: Intersecting brane worlds We review the construction of chiral four-dimensional compactifications of type IIA string theory with intersecting D6-branes. Such models lead to four-dimensional the- ories with non-abelian gauge interactions and charged chiral fermions. We discuss the application of these techniques to building of models with spectrum as close as possible to the Standard Model, and review their main phenomenological properties. 1Introduction String theory has the remarkable property that it provides a description of gauge and gravitational interactions in a unified framework consistently at the quantum level. It is this general feature (beyond other beautiful properties of particular string models) that makes this theory interesting as a possible candidate to unify our description of the different particles and interactions in Nature. Now if string theory is indeed realized in Nature, it should be able to lead not just to ‘gauge interactions’ in general, but rather to gauge sectors as rich and intricate as the gauge theory we know as the Standard Model of Particle Physics. In these lecture we describe compactifications of string theory where sets of D-branes lead to gauge sectors close to the Standard Model. We furthermore discuss the interplay of such D-brane systems with flux compactifications, recently introduced to address the issues of moduli stabilization and supersymmetry breaking. Before starting, it is important to emphasize that there are other constructions in string theory which are candidates to reproduce the physics of the Standard Model at low energies, which do not involve D-branes.
    [Show full text]
  • String Theory and M-Theory: a Modern Introduction Katrin Becker, Melanie Becker, and John H
    Cambridge University Press 978-0-521-86069-7 - String Theory and M-Theory: A Modern Introduction Katrin Becker, Melanie Becker, and John H. Schwarz Frontmatter More information STRING THEORY AND M-THEORY A MODERN INTRODUCTION String theory is one of the most exciting and challenging areas of modern theoretical physics. This book guides the reader from the basics of string theory to very recent developments at the frontier of string theory research. The book begins with the basics of perturbative string theory, world-sheet supersymmetry, space-time supersymmetry, conformal field theory and the heterotic string, and moves on to describe modern developments, including D-branes, string dualities and M-theory. It then covers string geometry (including Calabi–Yau compactifications) and flux compactifications, and applications to cosmology and particle physics. One chapter is dedicated to black holes in string theory and M-theory, and the microscopic origin of black-hole entropy. The book concludes by presenting matrix theory, AdS/CFT duality and its generalizations. This book is ideal for graduate students studying modern string theory, and it will make an excellent textbook for a 1-year course on string theory. It will also be useful for researchers interested in learning about developments in modern string theory. The book contains about 120 solved exercises, as well as about 200 homework problems, solutions of which are available for lecturers on a pass- word protected website at www.cambridge.org/9780521860697. K ATRIN B ECKER is a Professor of physics at Texas A & M University. She was awarded the Radcliffe Fellowship from Harvard University in 2006 and received the Alfred Sloan Fellowship in 2003.
    [Show full text]