DOCSLIB.ORG

Aspects of F-Theory-Engineered Quantum Field Theories

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Aspects of F-Theory-Engineered Quantum Field Theories Aspects of F-Theory-engineered Quantum Field Theories Memoria de Tesis Doctoral realizada por Federico Carta presentada ante el Departamento de F´ısicaTe´orica de la Universidad Aut´onomade Madrid para optar al T´ıtulode Doctor en F´ısicaTe´orica Tesis Doctoral dirigida por Dr. Fernando Marchesano, Cient´ıficoTitular del Instituto de F´ısicaTe´orica Departamento de F´ısicaTe´orica Universidad Aut´onomade Madrid Instituto de F´ısicaTe´oricaUAM/CSIC Mayo de 2018 Ai miei maestri. ABSTRACT In this thesis we discuss three examples of quantum field theories engineered from the IIB superstring theory and F-Theory. Firstly we consider a model of SU(5) GUT in F-Theory, with E7 enhancement. Yukawa couplings for the two heaviest families of MSSM are computed, as well as one CKM entry. Realistic masses for the fermions can be obtained by considering certain values of the parameters entering in the model. Secondly, we discuss the phenomenon of supersymmetry enhancement in QFTs, in which a theory with 4 supercharges flows in the IR to a theory with 8 supercharges. New systematic scans are performed in order to find more theories showing this peculiar feature. Furthermore, an explanation of this SUSY enhancement is given by geometrically engineering the QFT of a D3 probing a F-Theory singularity corresponding to a T-brane background. Thirdly, we consider mixed branches of 3d N = 4 QFTs. We devise a way to compute the Hilbert Series of a generic mixed branch of a particular set of theories of this kind, called T [SU(N)]. In order to understand how the usual formulae for a Coulomb Branch Hilbert series get modified in the mixed branch case, it was crucial to engineer the T [SU(N)] in IIB superstring theory, by the use of an Hanany-Witten setup. i RESUMEN En esta tesis damos de tres ejemplos de teorias cu´anticas de campos que pueden ser realizadas en la teor´ıade supercuerdas IIB, y teor´ıaF. Para empezar, consideramos un modelo modelo de Gran Unificaci´on(GUT) de grupo gauge SU(5) en teor´ıaF, con E7 enhancement. Se calculan los acoplos de Yukawa para las dos familias m´aspesadas del MSSM, como tambi´enuna entrada de la matriz CKM. Masas realistas para los fermiones pueden ser encontradas fijando algunos valores de los par´amentros que entran en el modelo. A continuaci´on,consideramos el fen´omenode incremento de supersimetr´ıaen Teor´ıasCu´anticas de Campos (QFTs), en que una teor´ıacon 4 supercargas fluye en el IR a una teor´ıacon 8 su- percargas. Hacemos nuevas b´usquedassistematicas para encontrar m´asteor´ıasque tienen esta propriedad particular. Adem´as,damos una explicaci´onde este fen´omeno a trav´esdel geometri- cal engineering de la QFT con una D3 que explora una singularidad en teor´ıaF que corresponde a una configuraci´ongauge no-Abeliana conocida como T-brana. Por ultimo, consideramos ramas mixtas de algunas teor´ıascu´anticas de campos 3d N = 4. Damos una manera para calcular la Serie de Hilbert de una cualquier rama mixta para un conjunto dado de teorias, llamadas T [SU(N)]. Para entender como se modifica la f´ormula de la Serie de Hilbert del Coulomb Branch en el caso de un mixed branch, es crucial pensar a la teor´ıa T [SU(N)] en el contexto de la teor´ıade supercuerdas IIB, a trav´esuna construcci´onde Hanany-Witten. ii ACKNOWLEDGEMENTS The first person I would like to thank is my supervisor, Fernando Marchesano, for having guided me through these years of the PhD. Thanks for having explained me numerous things in the field of String Phenomenology, having shared many interesting ideas with me, and having been always there when there was a need of any kind. It is a pleasure to have been your student! A second person I would like to thank is Hirotaka Hayashi. Basically everything I now know about the dynamics of supersymmetric QFTs, modulo a zero-mesure set of knowledge, I owe to him. I also thank him for having been an excellent collaborator over the years, always motivating me to proceed, in one way or another, trough the many struggles of scientific research. A third person I feel the urge to thank is Raffaele Savelli. Working with him I learned way too many interesting things in physics and mathematics, most importantly F-theory, which plays a major role in this thesis. Also thanks to the many other amazing collaborators I had over these years: Wieland, Gianluca, Simone, Cumrun and Daniel. It has been (and I am sure it will still be) a great opportunity and a great fun to work with all of you again. Thanks! I would like to thank the other seniors at the IFT, especially Luis and Angel, for all the physics related discussions, all the interesting conferences organized, and more importantly for having made the IFT a very enjoiable and stimulating environmenet to be in. Also thank you for writing The Book, which has been on my desk basically every day since I started this journey. Also, I would like to thank all the other students and postdocs at the Institute. The older generation, in particular Miguel, Irene, Ander, Gianluca, Sjoerd, Aitor, Wieland, Clemens, Francisco, Michael, Pramod and the newer generation as well. Thanks for having made, and still making the IFT a great and fun place! Especially important people in this PhD adventure have been my office mates: Paco, Sebastian, Eduardo and Nicol´o. With them I shared many everyday life moments, unforgettable discussions and trips around the world, during these years. Also special thanks to Eduardo, for helping me with the spanish chapters in this thesis. iii I would also like to thank Tom, Igor and Mirjam for having organized TASI 2017, as well as all the other speakers, students and people involved in that PhD school. TASI has been a unique experience for me: by far the most scientifically interesting and happiest month of my PhD life. I also feel the urge to acknowledge Isabel, Monica V, Monica E, Rebeca, Susana, Maria, Laura, Andr´es,Marcos, Emilio and all the other people working in the administration, outreach and IT at the IFT. The number of times they helped me during these years, and in verious different ways, is uncountable. Last but not least, I would like to thank my family: Rita, Marcello, Alice and Dario, zii e nonne. For all the love and support during these years, and always. iv CONTENTS 1 General Introduction 1 2 Yukawa couplings 5 2.1 The Standard Model and particles' masses. .5 2.2 Grand Unified Theories . .7 2.2.1 Gauge coupling unification . .8 2.2.2 Georgi-Glashow SU(5) GUT . .9 2.2.3 Anomaly cancellation. 11 2.2.4 GUTs' first prediction: Proton decay . 12 2.2.5 GUTs' second prediction: 't Hoft- Polyakov monopoles . 13 2.3 A brief introduction to F-Theory . 15 2.3.1 F-Theory from IIB superstring . 16 2.3.2 F-Theory from M-Theory . 18 2.3.3 F-Theory from Heterotic . 19 2.3.4 Elliptic curves, fibrations, and their singularities . 20 2.4 Yukawas and exceptional groups in F-theory GUTs . 23 2.4.1 SU(5) models with E7 enhancement . 27 2.4.2 Yukawa hierarchies in the E7 model . 29 2.4.3 Higgs background . 31 2.4.4 Primitive fluxes . 34 2.4.5 Residue formula for Yukawa couplings . 37 v 2.4.6 Holomorphic Yukawa couplings for the E7 model . 38 2.4.7 Normalization factors and physical Yukawas . 40 2.4.8 Perturbative wavefunctions . 41 2.4.9 Normalization factors . 43 2.4.10 Non-perturbative corrections to the wavefunctions . 44 2.4.11 Fitting fermion masses and mixing angles . 46 2.4.12 Fermion masses . 47 2.4.13 Quark mixing angles . 55 3 Supersymmetry enhancement 58 3.1 Generalities of 4d N = 2 QFTs . 58 3.2 The Seiberg-Witten curve. 63 3.3 Generalities of 4d N = 2 SCFTs. 65 3.4 Maruyoshi-Song flows. 71 3.5 New scans: looking for MS flows. 78 3.6 A geometric picture for the enhancement. 79 4 Mixed Branches of 3d N = 4 QFTs 85 4.1 3d field theories with 8 supercharges: generalities. 85 4.2 Quiver gauge theories . 92 4.3 A look at the moduli space . 94 4.4 Hilbert Series for Moduli Spaces of 3d N = 4 Theories . 96 4.4.1 Higgs branch moduli space . 97 4.4.2 Coulomb branch moduli space . 99 4.5 The Hanany-Witten cartoon . 100 4.6 3d mirror symmetry . 103 4.7 T [SU(N)] theory and its relation to class-S. 105 4.8 Mixed Branches of the T [SU(N)] Theory . 106 4.8.1 Hilbert series for the Coulomb branch factor . 112 4.8.2 Hilbert series for the Higgs branch factor . 114 4.8.3 The Restriction Rule for the Hilbert Series . 115 5 General conclusions 122 6 Conclusiones generales 128 vi 7 Appendices. 131 7.1 Dynkin Label notation . 131 7.2 E7 machinery . 132 7.3 Local chirality and doublet-triplet splitting . 135 7.3.1 Model A . 135 7.3.2 Model B . 136 7.4 Zero mode wavefunctions . 136 7.4.1 Wavefunctions in holomorphic gauge and Yukawa couplings . 136 7.4.2 Wavefunctions in real gauge . 138 7.4.3 Holomorphic Yukawa matrix . 145 7.5 Coulomb branch examples of restriction rule. 146 7.6 Higgs branch examples of the restriction rule . 158 7.7 Nilpotent Orbits . 165 7.7.1 A sketch of the classification .
Load more

Recommended publications
  • Bosonization and Mirror Symmetry Arxiv:1608.05077V1 [Hep-Th]
    Bosonization and Mirror Symmetry Shamit Kachru1, Michael Mulligan2,1, Gonzalo Torroba3, and Huajia Wang4 1Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA 94305, USA 2Department of Physics and Astronomy, University of California, Riverside, CA 92511, USA 3Centro At´omico Bariloche and CONICET, R8402AGP Bariloche, ARG 4Department of Physics, University of Illinois, Urbana-Champaign, IL 61801, USA Abstract We study bosonization in 2+1 dimensions using mirror symmetry, a duality that relates pairs of supersymmetric theories. Upon breaking supersymmetry in a controlled way, we dynamically obtain the bosonization duality that equates the theory of a free Dirac fermion to QED3 with a single scalar boson. This duality may be used to demonstrate the bosonization duality relating an O(2)-symmetric Wilson-Fisher fixed point to QED3 with a single Dirac fermion, Peskin-Dasgupta-Halperin duality, and the recently conjectured duality relating the theory of a free Dirac fermion to fermionic QED3 with a single flavor. Chern-Simons and BF couplings for both dynamical and background gauge fields play a central role in our approach. In the course of our study, we describe a \chiral" mirror pair that may be viewed as the minimal supersymmetric generalization of the two bosonization dualities. arXiv:1608.05077v1 [hep-th] 17 Aug 2016 Contents 1 Introduction 1 2 Mirror symmetry and its deformations 4 2.1 Superfields and lagrangians . .5 2.2 = 4 mirror symmetry . .7 N 2.3 Deformations by U(1)A and U(1)R backgrounds . 10 2.4 General mirror duality . 11 3 Chiral mirror symmetry 12 3.1 Chiral theory A .
    [Show full text]
  • Arxiv:2002.11085V1 [Hep-Th]
    On-Shell Electric-Magnetic Duality and the Dual Graviton 1,2 2 Nathan Moynihan and Jeff Murugan ∗ 1High Energy Physics, Cosmology & Astrophysics Theory group, 2The Laboratory for Quantum Gravity & Strings Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, Cape Town 7700, South Africa Using on-shell amplitude methods, we explore 4-dimensional Electric-Magnetic duality and its double copy. We show explicitly that the on-shell scattering amplitudes know about ‘dual’ photons (and dual gravitons), that the off-shell photon propagator double copies to the graviton propagator and that the magnetic part of the propagator is essential for the double copy to hold. We also show that there is an equivalent gravito-magnetic part of the graviton propagator which is essential in giving rise to solutions with either angular momentum or NUT charge. Furthermore, we comment on the so-called Weinberg paradox, which states that scattering amplitudes involving the mixing of electric and magnetic monopoles cannot be Lorentz invariant, and would seem to preclude the existence of the ’t Hooft-Polyakov (topological) monopole. We trace this paradox to the magnetic part of the propagator, showing that it can be eliminated if one restricts to proper orthochronous Lorentz transformations. Finally, we compute the fully relativistic cross-section for arbitrary spin dyons using the recently formulated on-shell duality transformation and show that this is always fully Lorentz invariant. INTRODUCTION field theory without a Dirac string singularity necessitates the introduction of a second four-vector potential: the The boostrap program of the 1960’s received considerable dual photon [3–6].
    [Show full text]
  • Large N Free Energy of 3D N=4 Scfts and Ads/CFT Benjamin Assel, John Estes, Masahito Yamazaki
    Large N Free Energy of 3d N=4 SCFTs and AdS/CFT Benjamin Assel, John Estes, Masahito Yamazaki To cite this version: Benjamin Assel, John Estes, Masahito Yamazaki. Large N Free Energy of 3d N=4 SCFTs and AdS/CFT. Journal of High Energy Physics, Springer, 2012, pp.074. 10.1007/JHEP09(2012)074. hal-00718824 HAL Id: hal-00718824 https://hal.archives-ouvertes.fr/hal-00718824 Submitted on 18 Jul 2012 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. LPTENS-12/23 PUPT-2418 Large N Free Energy of 3d = 4 SCFTs and N AdS4/CFT3 Benjamin Assel\, John Estes[ and Masahito Yamazaki] \ Laboratoire de Physique Th´eoriquede l'Ecole´ Normale Sup´erieure, 24 rue Lhomond, 75231 Paris cedex, France [ Instituut voor Theoretische Fysica, KU Leuven, Celestijnenlaan 200D B-3001 Leuven, Belgium ] Princeton Center for Theoretical Science, Princeton University, Princeton, NJ 08544, USA Abstract We provide a non-trivial check of the AdS4/CFT3 correspondence recently proposed in [1] by verifying the GKPW relation in the large N limit. The CFT free energy is obtained from the previous works [2, 3] on the S3 partition function for 3-dimensional = 4 SCFT T [SU(N)].
    [Show full text]
  • Ads₄/CFT₃ and Quantum Gravity
    AdS/CFT and quantum gravity Ioannis Lavdas To cite this version: Ioannis Lavdas. AdS/CFT and quantum gravity. Mathematical Physics [math-ph]. Université Paris sciences et lettres, 2019. English. NNT : 2019PSLEE041. tel-02966558 HAL Id: tel-02966558 https://tel.archives-ouvertes.fr/tel-02966558 Submitted on 14 Oct 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Prepar´ ee´ a` l’Ecole´ Normale Superieure´ AdS4/CF T3 and Quantum Gravity Soutenue par Composition du jury : Ioannis Lavdas Costas BACHAS Le 03 octobre 2019 Ecole´ Normale Superieure Directeur de These Guillaume BOSSARD Ecole´ Polytechnique Membre du Jury o Ecole´ doctorale n 564 Elias KIRITSIS Universite´ Paris-Diderot et Universite´ de Rapporteur Physique en ˆIle-de-France Crete´ Michela PETRINI Sorbonne Universite´ President´ du Jury Nicholas WARNER University of Southern California Membre du Jury Specialit´ e´ Alberto ZAFFARONI Physique Theorique´ Universita´ Milano-Bicocca Rapporteur Contents Introduction 1 I 3d N = 4 Superconformal Theories and type IIB Supergravity Duals6 1 3d N = 4 Superconformal Theories7 1.1 N = 4 supersymmetric gauge theories in three dimensions..............7 1.2 Linear quivers and their Brane Realizations...................... 10 1.3 Moduli Space and Symmetries............................
    [Show full text]
  • Arxiv:Hep-Th/9902033V2 1 Apr 1999
    IASSNS–HEP–99/15 hep-th/9902033 On Mirror Symmetry in Three Dimensional Abelian Gauge Theories Anton Kapustin and Matthew J. Strassler School of Natural Sciences, Institute for Advanced Study, Olden Lane, Princeton, NJ 08540, USA kapustin, [email protected] Abstract We present an identity relating the partition function of = 4 supersym- N metric QED to that of its dual under mirror symmetry. The identity is a gen- eralized Fourier transform. Many known properties of abelian theories can be derived from this formula, including the mirror transforms for more general gauge and matter content. We show that = 3 Chern-Simons QED and N = 4 QED with BF-type couplings are conformal field theories with exactly N marginal couplings. Mirror symmetry acts on these theories as strong-weak coupling duality. After identifying the mirror of the gauge coupling (some- times called the “magnetic coupling”) we construct a theory which is exactly mirror — at all scales — to = 4 SQED. We also study vortex-creation N operators in the large Nf limit. arXiv:hep-th/9902033v2 1 Apr 1999 1 I. INTRODUCTION Major advances in supersymmetric field theory and string theory in various dimensions have led to the understanding that it is common for apparently different quantum field theories to be quantum-mechanically equivalent. Two theories which are “dual” in this way may be thought of as two choices of variables in a path integral representation for the same generating functional. Not that such “duality relations” are new; the relation between position space and momentum space representations of quantum mechanical systems are of this type; the order-disorder-fermion representations of the Ising model, the identity of the sine-Gordon model and the Thirring model, and target-space duality in two-dimensional sigma-models are well known from two dimensions; and it has long been conjectured that = 4 supersymmetric Yang-Mills theory in four dimensions is a conformal field theory with aN duality symmetry.
    [Show full text]
  • Spontaneous Symmetry Breaking in Free Theories with Boundary
    SciPost Phys. 11, 035 (2021) Spontaneous symmetry breaking in free theories with boundary potentials Vladimir Procházka? and Alexander Söderberg† Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala, Sweden ? [email protected],† [email protected] Abstract Patterns of symmetry breaking induced by potentials at the boundary of free O(N)- models in d = 3 ε dimensions are studied. We show that the spontaneous symmetry breaking in these− theories leads to a boundary RG flow ending with N 1 Neumann modes in the IR. The possibility of fluctuation-induced symmetry breaking− is examined and we derive a general formula for computing one-loop effective potentials at the boundary. Using the ε-expansion we test these ideas in an O(N) O(N)-model with boundary in- teractions. We determine the RG flow diagram of this⊕ theory and find that it has an IR- stable critical point satisfying conformal boundary conditions. The leading correction to the effective potential is computed and we argue the existence of a phase boundary separating the region flowing to the symmetric fixed point from the region flowing to a symmetry-broken phase with a combination of Neumann and Dirchlet boundary condi- tions. Copyright V.Procházka and A. Söderberg. Received 08-04-2021 This work is licensed under the Creative Commons Accepted 28-07-2021 Check for Attribution 4.0 International License. Published 19-08-2021 updates Published by the SciPost Foundation. doi:10.21468/SciPostPhys.11.2.035 Contents 1 Introduction2 2 One loop effective boundary potentials5 3 O(Nφ) O(Nχ ) scalar model7 3.1 The⊕ model7 3.2 Coleman-Weinberg mechanism9 4 Conclusion 12 A Propagators in boundary quantum field theories 13 A.1 In spacetime coordinates 14 A.2 Momentum propagator 16 B β-function 18 C Functional determinants 20 References 22 1 SciPost Phys.
    [Show full text]
  • Hagedorn Transition, Vortices and D0 Branes: Lessons from 2+1 Confining
    CERN-TH/2001-088 MIT-CTP-3095 hep-th/0103235 Hagedorn transition, vortices and D0 branes: Lessons from 2+1 confining strings. Ian I. Kogana1, Alex Kovnerb,c2, Martin Schvellingera,d3 aTheoretical Physics, Department of Physics, University of Oxford, 1 Keble Road, Oxford, OX1 3NP, UK bTheory Division, CERN, CH-1211, Geneva 23, Switzerland cDepartment of Mathematics and Statistics, University of Plymouth, Plymouth PL4 8AA, UK dCenter for Theoretical Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge MA 02139, USA Abstract We study the behaviour of Polyakov confining string in the Georgi-Glashow model in three dimensions near confining-deconfining phase transition described in [33]. In the string language, the transition mechanism is the decay of the confining string into D0 branes (charged W ± bosons of the Georgi-Glashow model). In the world-sheet picture the world-lines of heavy D0 branes at finite temperature are represented as world-sheet vortices of a certain type, and the transition corresponds to the condensation of these vortices. We also show that the \would be" Hagedorn transition in the confining string (which is not realized in our model) corresponds to the monopole binding transition in the field theoretical language. The fact that the decay into D0 branes occurs at lower than the Hagedorn temperature is understood as the consequence of the large thickness of the confining string and finite mass of the D0branes. CERN-TH/2001-088 Keywords: Confining Strings, Vortices, Confinement [email protected] [email protected] [email protected] 1 Introduction What happens to strings at very high temperatures is one of the Big questions of string theory.
    [Show full text]
  • String Theory, the Dark Sector, and the Hierarchy Problem
    Letters in High Energy Physics LHEP-186, 2021 String Theory, the Dark Sector, and the Hierarchy Problem Per Berglund,1 Tristan H¨ubsch,2 and Djordje Minic3 1Department of Physics and Astronomy, University of New Hampshire, Durham, NH 03824, USA 2Department of Physics and Astronomy, Howard University, Washington, DC 20059, USA 3Department of Physics, Virginia Tech, Blacksburg, VA24061, USA Abstract We discuss dark energy, dark matter, and the hierarchy problem in the context of a general noncommuta- tive formulation of string theory. In this framework, dark energy is generated by the dynamical geometry of the dual spacetime while dark matter, on the other hand, comes from the degrees of freedom dual to the visible matter. This formulation of string theory is sensitive to both the IR and UV scales, and the Higgs scale is radiatively stable by being a geometric mean of radiatively stable UV and IR scales. We also com- ment on various phenomenological signatures of this novel approach to dark energy, dark matter, and the hierarchy problem. We find that this new view on the hierarchy problem is realized in a toy model based on a nonholomorphic deformation of the stringy cosmic string. Finally, we discuss a proposal for a new nonperturbative formulation of string theory, which sheds light on M-theory and F-theory, as well as on supersymmetry and holography. Keywords: string theory, dark energy, dark matter, hierarchy ical signatures stemming from this correlation. We also com- problem ment about other phenomenological signatures of this new ap- DOI: 10.31526/LHEP.2021.186 proach to dark energy, dark matter, and the hierarchy problem in the context of string theory.
    [Show full text]
  • Confinement in Yang{Mills: Elements of a Big Picture
    October 2008 UMN-TH-2720/08 , FTPI-MINN-08/38 , SLAC-PUB-13434 Confinement in Yang{Mills: Elements of a Big Picture M. Shifmana;b and Mithat Unsal• c;d a William I. Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, MN 55455, USA b Laboratoire de Physique Th´eorique1 Universit´ede Paris-Sud XI Bˆatiment 210, F-91405 Orsay C´edex,FRANCE c SLAC, Stanford University, Menlo Park, CA 94025, USA d Physics Department, Stanford University, Stanford, CA,94305, USA Abstract This is a combined and slightly expanded version of talks deliv- ered at 14th International QCD Conference “QCD 08,” 7-12th July 2008, Montpellier, France, the International Conference “Quark Con- finement and the Hadron Spectrum,” Mainz, Germany, September 1-6, 2008 (Confinement 08), and the International Conference “Approaches to Quantum Chromodynamics,” Oberw•olz,Austria, September 7-13, 2008. Work supported in part by US Department of Energy contract DE-AC02-76SF00515 1UniteMixte de Recherche du CNRS, (UMR 8627). 1 Introduction QCD is a non-Abelian gauge theory of strong interactions. It is extremely rich and describes a very wide range of natural phenomena, e.g.: all of nuclear physics; Regge behavior and Regge trajectories; strongly coupled quark-gluon plasma; high-T and high-density phenom- ena; neutron stars; richness of the hadronic world (chiral phenomena, light and heavy quarkonia, glueballs and exotics, exclusive and inclusive processes, interplay between strong and weak interactions, and many other issues). At short distances QCD is weakly coupled, allowing high precision pertur- bative (multi-loop, multi-leg) calculations, however, analytical computations at all energy and momentum scales seem unlikely due to strong coupling nature at large distances.
    [Show full text]
  • Quantum Dynamics of Supergravity
    Quantum Dynamics of Supergravity David Tong Work with Carl Turner Based on arXiv:1408.3418 Crete, September 2014 1 2GM 2GM − distance2 = 1 δt2 + 1 dr2 + r2 δθ2 +sin2 θδφ2 − − rc2 − rc2 x = R sin θ sin φ y = R sin θ cos φ z = R cos θ δx =(R cos θ sin φ)δθ +(R sin θ cos φ)δφ δy =(R cos θ cos φ)δθ (R sin θ sin φ)δφ − δz = (R sin θ)δθ − θ φ Acknowledgement My thanks to Nick Dorey for many useful discussions. I’m supported by the Royal Society. An Old Idea: Euclidean Quantum Gravity References [1] J. Polchinski, “Dirichlet-Branes and Ramond-Ramond Charges,” Phys. Rev. Lett. 75, 4724 (1995) [arXiv:hep-th/9510017]. = g exp d4x √g Z D − R topology 17 1 2GM 2GM − distance2 = 1 δt2 + 1 dr2 + r2 δθ2 +sin2 θδφ2 − − rc2 − rc2 x = R sin θ sin φ y = R sin θ cos φ z = R cos θ δx =(R cos θ sin φ)δθ +(R sin θ cos φ)δφ δy =(R cos θ cos φ)δθ (R sin θ sin φ)δφ − δz = (R sin θ)δθ − θ A Preview of the Main Results φ 1,d 1 1 Kaluza-Klein Theory: = R − S M × 1 ∂ σ = F νρ µ 2 µνρ Λ M grav pl R Acknowledgement My thanks to Nick Dorey for many useful discussions. I’m supported by the Royal Society.There is a long history of quantum instabilities of these backgrounds • Casimir Forces References • Tunneling to “Nothing” Appelquist and Chodos ‘83 [1] J.
    [Show full text]
  • Conifold Transitions and Five-Brane Condensation in M-Theory on Spin(7
    INSTITUTE OF PHYSICS PUBLISHING CLASSICAL AND QUANTUM GRAVITY Class. Quantum Grav. 20 (2003) 665–705 PII: S0264-9381(03)53801-1 Conifold transitions and five-brane condensation in M-theory on Spin(7) manifolds Sergei Gukov1,JamesSparks2 and David Tong3 1 Jefferson Physical Laboratory, Harvard University, Cambridge, MA 02138, USA 2 Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK 3 Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA E-mail: [email protected], [email protected] and [email protected] Received 23 September 2002, in final form 6 January 2003 Published 28 January 2003 Online at stacks.iop.org/CQG/20/665 Abstract We conjecture a topology-changing transition in M-theory on a non-compact asymptotically conical Spin(7) manifold, where a 5-sphere collapses and a CP2 bolt grows. We argue that the transition may be understood as the condensation of M5-branes wrapping S5.Upon reduction to ten dimensions, it has a physical interpretation as a transition of D6-branes lying on calibrated submanifolds of flat space. In yet another guise, it may be seen as a geometric transition between two phases of type IIA string theory on a G2 holonomy manifold with either wrapped D6-branes, or background Ramond–Ramond flux. This is the first non-trivial example of a topology-changing transition with only 1/16 supersymmetry. PACS numbers: 11.25.Mj, 11.30.Pb, 11.15.Tk Contents 1. Introduction 666 2. D6-branes, M-theory and Spin(7) conifolds 670 2.1.
    [Show full text]
  • Black Branes in Flux Compactifications
    SLAC-PUB-15462, SU-ITP-13/07 Black branes in flux compactifications Gonzalo Torroba and Huajia Wang Stanford Institute for Theoretical Physics Department of Physics, Stanford University Stanford, CA 94305, USA Theory Group, SLAC National Accelerator Laboratory Menlo Park, CA 94309, USA Abstract We construct charged black branes in type IIA flux compactifications that are dual to (2 + 1){dimensional field theories at finite density. The internal space is a general Calabi-Yau manifold with fluxes, with internal dimensions much smaller than the AdS radius. Gauge fields descend from the 3-form RR potential evaluated on harmonic forms of the Calabi-Yau, and Kaluza-Klein modes decouple. Black branes are described by a four-dimensional effective field theory that includes only a few light fields and is valid over a parametrically large range of scales. This effective theory determines the low energy dynamics, stability and thermodynamic properties. Tools from flux compactifications are also used to construct holographic CFTs with no relevant scalar operators, that can lead to symmetric phases of condensed matter systems stable to very low temperatures. The general formalism is illustrated with simple examples such as toroidal compactifications and manifolds with a single size modulus. We initiate the classification of holographic phases of matter described by flux compactifications, 2 which include generalized Reissner-Nordstrom branes, nonsupersymmetric AdS2 × R and hyperscaling violating solutions. Published in arXiv:1306.3982. Work supported in part by US Department of Energy contract DE-AC02-76SF00515. Contents 1 Introduction 1 1.1 Basic setup and structure of the paper . 3 2 Type IIA compactifications, gauge fields and holography 4 2.1 Review of ten-dimensional supergravity and compactification .
    [Show full text]