Gravity duality foundations and applications

Front Cover

Front Matter

Contents

Preface

Acknowledgements

Part I. Prerequisites

1. Elements of Field Theory
- 1.1 Classical scalar field theory
- 1.2 Symmetries and conserved currents
- 1.3 Quantisation
- 1.4 Wick rotation and statistical mechanics
- 1.5 Regularisation and renormalisation
- 1.6 Dirac fermions
- 1.7 Gauge theory
- 1.8 Symmetries, Ward identities and anomalies
- 1.9 Further reading
2. Elements of Gravity
- 2.1 Differential geometry
- 2.2 Einstein’s field equations
- 2.3 Maximally symmetric spacetimes
- 2.4 Black holes
- 2.5 Energy conditions
3. Symmetries in Quantum Field Theory
- 3.1 Lorentz and Poincaré symmetry
- 3.2 Conformal symmetry
- 3.3 Supersymmetry
- 3.4 Superconformal symmetry
4. Introduction to Superstring Theory
- 4.1 Bosonic string theory
- 4.2 Superstring theory
- 4.3 Web of dualities
- 4.4 D-branes and other non-perturbative objects

Part II. Gauge/Gravity Duality

5. The AdS/CFT Correspondence
- 5.1 The AdS/CFT correspondence: a first glance
- 5.2 D3-branes and their two faces
- 5.3 Field-operator map
- 5.4 Correlation functions
- 5.5 Holographic renormalisation
- 5.6 Wilson loops in N = 4 Super Yang–Mills theory
6. Tests of the AdS/CFT Correspondence
- 6.1 Correlation function of 1/2 BPS operators
- 6.2 Four-point functions
- 6.3 The conformal anomaly
7. Integrability and Scattering Amplitudes
- 7.1 Integrable structures on the gauge theory side
- 7.2 Integrability on the gravity (string theory) side
- 7.3 BMN limit and classical string configurations
- 7.4 Dual superconformal symmetry
8. Further Examples of the AdS/CFT Correspondence
- 8.1 D3-branes at singularities
- 8.2 M2-branes: AdS4/CFT3
- 8.3 Gravity duals of conformal field theories: further examples
- 8.4 Towards non-conformal field theories
9. Holographic Renormalisation Group Flows
- 9.1 Renormalisation group flows in quantum field theory
- 9.2 Holographic renormalisation group flows
- 9.3 ∗Supersymmetric flows within IIB Supergravity in D = 10
10. Duality with D-Branes in Supergravity
- 10.1 Branes as flavour degrees of freedom
- 10.2 AdS/CFT correspondence with probe branes
- 10.3 D7-brane fluctuations and mesons in N = 2 theory
- 10.4 ∗D3/D5-brane system
11. Finite Temperature and Density
- 11.1 Finite temperature field theory
- 11.2 Gravity dual thermodynamics
- 11.3 Finite density and chemical potential

Part III. Applications

12. Linear Response and Hydrodynamics
- 12.1 Linear response
- 12.2 Hydrodynamics
- 12.3 Transport coefficients from linear response
- 12.4 Fluid/gravity correspondence
13. QCD and Holography: Confinement and Chiral Symmetry Breaking
- 13.1 Review of QCD
- 13.2 Gauge/gravity duality description of confinement
- 13.3 Chiral symmetry breaking from D7-brane probes
- 13.4 Non-Abelian chiral symmetries: the Sakai–Sugimoto model
- 13.5 AdS/QCD correspondence
14. QCD and Holography: Finite Temperature and Density
- 14.1 QCD at finite temperature and density
- 14.2 Gauge/gravity approach to the quark–gluon plasma
- 14.3 Holographic flavour at finite temperature and density
- 14.4 Sakai–Sugimoto model at finite temperature
- 14.5 Holographic predictions for the quark–gluon plasma
15. Strongly Coupled Condensed Matter Systems
- 15.1 Quantum phase transitions
- 15.2 Charges and finite density
- 15.3 Holographic superfluids and superconductors
- 15.4 Fermions
- 15.5 Towards non-relativistic systems and hyperscaling violation
- 15.6 Entanglement entropy

Appendix A. Grassmann Numbers

Appendix B. Lie Algebras and Superalgebras

Appendix C. Conventions

Index