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Table of contents
Introduction
1 Elements of the AdS/CFT correspondence
1.1 Superconformal field theories
1.1.1 N = 4 SYM
1.2 String theory and supergravity
1.3 Statement of the correspondence
1.3.1 Computing correlators
1.4 Generalizations of the correspondence
1.4.1 Finite temperature
1.4.2 Finite density
1.4.3 Flavor degrees of freedom
1.5 Theories with unquenched flavor degrees of freedom
2 Holographic hydrodynamics
2.1 Classical and supersymmetric hydrodynamics
2.2 Response theory and Kubo formulas
2.3 Transport coefficients in AdS/CFT
2.3.1 Universality of the shear viscosity to entropy ratio
2.4 The supercurrent correlator in supergravity
2.5 Supercharge diffusion at finite temperature
2.5.1 Running of the correlator
2.6 Supercharge diffusion at finite density
2.6.1 The background
2.6.2 Analytic solution for small charge
2.6.3 Numerical Solution
3 Holographic entanglement entropy
3.1 Entanglement entropy in field theory
3.1.1 Mass corrections in the waveguide geometry
3.2 The holographic prescription
3.2.1 Review of the pure AdS case
3.3 Corrections from massive flavor degrees of freedom
3.3.1 The slab case
3.3.2 The ball case
Conclusions and perspectives
A Gamma matrix conventions
B Normalization of the boundary action
C Résumé détaillé (en français)
C.1 Introduction
C.2 Elements de la correspondance AdS/CFT
C.3 Hydrodynamique holographique
C.4 Entropie d’intrication holographique
C.5 Conclusions et perspectives
Bibliography
