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Lecture Notes in Physics

The Ads/CFT Correspondence

By: Eleftherios Papantonopoulos (Editor)

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Paperback | 26 March 2011

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The AdS/CFT correspondence is a powerful tool in studying strongly coupled phenomena in gauge field theories, using results from a weakly coupled gravity background studied in the realm of string theory. AdS/CFT was first successfully applied to the study of phenomena such as the quark-gluon plasma produced in heavy ions collisions. Soon it was realized that its applicability can be extended, in a more phenomenological approach, to condensed matter systems and to systems described by fluid dynamics.

The set of tutorial reviews in this volume is intended as an introduction to and survey of the principle of the AdS/CFT correspondence in its field/string theoretic formulation, its applicability to holographic QCD and to heavy ions collisions, and to give a first account of processes in fluid dynamics and condensed matter physics, which can be studied with the use of this principle.

Written by leading researchers in the field and cast into the form of a high-level but approachable multi-author textbook, this volume will be of benefit to all postgraduate students, and newcomers from neighboring disciplines wishing to find a comprehensive guide for their future research.

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Non-Fiction Science Physics Classical Mathematics Gravity Quantum Physics & Quantum Mechanics & Quantum Field Theory Applied Physics Geophysics Statistical Physics Materials & States of Matter Relativity Physics

Introduction to the AdS/CFT Correspondence
Introduction to Anti de Sitter Black Holes	p. 3
Spacetimes of Constant Curvature	p. 3
Spaces of Maximal Symmetry and Constant Curvature	p. 3
Flat Spacetime	p. 5
Anti de Sitter Spacetime	p. 7
Static Black Holes	p. 15
Basic Properties	p. 15
Thermodynamics	p. 18
Beyond Static Black Holes	p. 21
References	p. 25
Perturbations of Anti de Sitter Black Holes	p. 27
Introduction	p. 27
Perturbations	p. 28
Scalar Perturbations	p. 29
Gravitational Perturbations	p. 32
Electromagnetic Perturbations	p. 37
Hydrodynamics	p. 38
Vector Perturbations	p. 38
Scalar Perturbations	p. 43
Tensor Perturbations	p. 46
Hydrodynamics on the AdS boundary	p. 47
Conformal Soliton Flow	p. 48
Phase Transitions	p. 49
K = 0	p. 49
K = -1	p. 51
Conclusion	p. 55
References	p. 55
Introduction to the AdS/CFT Correspondence	p. 57
Introduction	p. 57
CFTs	p. 58
Conformal Algebra	p. 58
Local Field Operators	p. 59
Conformal Correlators	p. 60
AdS/CFT Correspondence	p. 62
AdS Geometry	p. 62
Partition Function	p. 64
Semi-classical Gravity Limit	p. 65
Large N	p. 67
D3-Branes and AdS₅ × S⁵	p. 68
SYM from D-Branes	p. 69
D3-Brane Near Horizon Geometry	p. 70
Strong/Weak Duality	p. 71
Extensions	p. 72
References	p. 74
Holography and the AdS/CFT Correspondence
Improved Holographic QCD	p. 79
Introduction	p. 80
The 5D Model	p. 85
Scheme Dependence	p. 88
The Potential and the Parameters of the Model	p. 91
The Normalization of the Coupling Constant	p. 92
The AdS Scale l	p. 93
The UV Expansion Coefficients of V()	p. 93
The 5D Planck Scale M_P	p. 94
The String Length	p. 95
Integration Constants	p. 95
Matching the Thermodynamics of Large-N_c YM	p. 96
Latent Heat and Equation of State	p. 99
Glueball Spectrum	p. 101
Critical Temperature	p. 103
String Tension	p. 104
CP-odd Sector	p. 105
Coupling Normalization	p. 107
Bulk Viscosity	p. 108
The Holographic Computation	p. 109
Holographic Explanation for the Rise of /s Near T_c	p. 113
The Adiabatic Approximation	p. 116
Buchel's Bound	p. 118
The Drag Force on Strings and Heavy Quarks	p. 120
The Drag Force	p. 122
The Relativistic Asymptotics	p. 124
The Non-relativistic Asymptotics	p. 126
The Diffusion Time	p. 126
Including the Correction to the Quark Mass	p. 127
Temperature Matching and Diffusion Time Estimates	p. 129
Jet Quenching Parameter	p. 132
Discussion and Outlook	p. 139
Bulk Viscosity	p. 140
Drag Force	p. 141
Diffusion Time	p. 141
Jet Quenching	p. 141
References	p. 142
The Dynamics of Quark-Gluon Plasma and AdS/CFT	p. 147
Introduction	p. 147
The AdS/CFT Correspondence	p. 150
Effective Degrees of Freedom at Strong Coupling	p. 150
Why study N = 4 Plasma?	p. 151
The AdS/CFT for Studying Real-Time Dynamics of Plasma	p. 152
The Gravity → (T) Dictionary	p. 154
The (T) → Gravity Dictionary	p. 154
Exact Analytical Examples	p. 155
A Case Study: Static Uniform Plasma	p. 156
A Case Study: A Planar Shock Wave	p. 159
Boost-Invariant Flow	p. 159
Large Proper Time Behaviour	p. 161
The AdS/CFT Analysis	p. 162
Perfect Fluid Geometry	p. 164
Plasma Dynamics Beyond Perfect Fluid	p. 165
Interlude: Hydrodynamics Redux	p. 167
Plasma Dynamics Beyond Hydrodynamics	p. 169
Dynamics at Small Proper Time	p. 170
The Absence of a Scaling Variable	p. 170
The Existence of a Regular Initial Condition	p. 171
The Classification of Possible Initial Conditions	p. 172
An Analysis of Some Aspects of the Small Proper Time Behaviour of ()	p. 174
Conclusions	p. 175
Appendix	p. 177
References	p. 178
Fluid Dynamics from Gravity	p. 183
Introduction	p. 183
Quantum Gravity	p. 184
Universal Implications	p. 185
QCD	p. 185
Fluid Dynamics	p. 186
Background	p. 187
Conformal Fluid Dynamics	p. 187
Gravity in the Bulk	p. 188
Fluid/Gravity Map	p. 189
Construction of Bulk Metric and Boundary Stress Tensor	p. 191
0th Order	p. 191
1st Order	p. 192
Solution to Second Order	p. 194
The Four-Dimensional Conformal Fluid from AdS₅	p. 195
The Spacetime Geometry Dual to Fluids	p. 196
Summary	p. 199
References	p. 202
The Gauge-Gravity Duality and Heavy Ion Collisions	p. 205
The Wake of a Quark	p. 206
Jet Correlations at RHIC	p. 206
A Holographic Computation	p. 208
Entropy Production	p. 219
References	p. 230
AdS/CFT on the Brane	p. 235
Introduction	p. 235
Braneworlds in AdS Spacetime	p. 237
RS Models	p. 237
Cosmology	p. 238
View from the Brane	p. 241
AdS/CFT Correspondence	p. 241
Geometrical Holography	p. 242
Does AdS/CFT Play Any Role in Braneworld?	p. 243
Single-Brane Model	p. 244
Two-Brane Model	p. 245
Gradient Expansion Method	p. 245
Single Brane Model (RS2)	p. 248
Einstein Gravity at Lowest Order	p. 248
AdS/CFT Emerges	p. 250
Two-Brane Model (RS1)	p. 253
Scalar-Tensor Theory Emerges	p. 253
AdS/CFT in Two-Brane System?	p. 254
The Answers	p. 258
Single-Brane Model	p. 258
Two-Brane Model	p. 259
AdS/CFT in Dilatonic Braneworld	p. 260
Dilatonic Braneworld	p. 261
AdS/Radion Correspondence	p. 262
AdS/CFT and KK Corrections: Single-Brane Cases	p. 267
Conclusion	p. 267
References	p. 268
Condensed Matter and the AdS/CFT Correspondence
Condensed Matter and AdS/CFT	p. 273
Introduction	p. 273
Model Systems and Their Critical Theories	p. 275
Coupled Dimer Antiferromagnets	p. 275
Deconfined Criticality	p. 276
Graphene	p. 278
Finite Temperature Crossovers	p. 279
Quantum Critical Transport	p. 282
Exact Results for Quantum Critical Transport	p. 285
Hydrodynamic Theory	p. 287
Relativistic Magnetohydrodynamics	p. 288
Dyonic Black Hole	p. 289
Results	p. 290
d-wave Superconductors	p. 292
Dirac Fermions	p. 292
Time-Reversal Symmetry Breaking	p. 294
Nematic Ordering	p. 299
Metals	p. 300
Field Theories	p. 303
Symmetries	p. 303
Scaling Theory	p. 305
Large N Expansion	p. 306
AdS/CFT Correspondence	p. 308
References	p. 309
Introduction to Holographic Superconductors	p. 313
Introduction	p. 313
Superconductivity	p. 314
A Gravitational Dual	p. 316
Probe Limit	p. 318
Condensate	p. 318
Conductivity	p. 324
Full Solution with Backreaction	p. 327
Reformulation of the Conductivity	p. 330
Zero Temperature Limit	p. 332
m² = 0	p. 333
q² >
Adding Magnetic Fields	p. 336
London Equation	p. 338
Correlation Length	p. 339
Vortices	p. 339
Recent Developments	p. 340
Conclusions and Open Problems	p. 342
Open Problems	p. 343
References	p. 344
Flavor Superconductivity and Superfluidity	p. 349
Introduction	p. 349
String Motivation	p. 350
Condensed Matter Motivation	p. 351
Superconductivity and Holography	p. 352
Basics of Superconductivity and Our Field Theory Idea	p. 352
Holographic Realization	p. 356
Holographic Setup	p. 358
Flavor from Intersecting Branes	p. 358
Background and Brane Configuration	p. 363
DBI Action and Equations of Motion	p. 365
D-Brane Thermodynamics and Spectrum	p. 371
Baryon Chemical Potential	p. 371
Isospin Chemical Potential	p. 375
Instabilities and the New Phase	p. 376
Signatures of Super-Something	p. 376
Thermodynamics of the Broken Phase	p. 376
Fluctuations in the Broken Phase	p. 380
Conductivity and Spectrum	p. 383
Meissner-Ochsenfeld-Effect	p. 384
Interpretation and Conclusion	p. 389
String Theory Picture	p. 389
Summary	p. 390
Outlook	p. 391
References	p. 392
Holographic Torsion and the Prelude to Kalb-Ramond Superconductivity	p. 395
Introduction and Summary of the Results	p. 395
Torsion as the Non-trivial Magnetic Field of Gravity	p. 397
Electromagnetism with a (x)-Angle in AdS₄	p. 397
Details on the the 3 + 1-Split Formalism	p. 399
The Analog of -Angle in Gravity	p. 402
Torsion and the Magnetic Field of Gravity	p. 403
The Nieh-Yan Models	p. 404
General Aspects	p. 404
The 3 + 1-Split of the Pseudoscalar Nieh-Yan Model	p. 406
The Torsion Domain Wall	p. 407
The Gravity Dual of Parity Symmetry Breaking	p. 410
Physics in the Bulk: The Superconductor Analogy	p. 412
Torsion Domain Wall Versus Abrikosov Vortex	p. 413
Domain Wall Condensation	p. 414
Conclusions	p. 417
Appendix	p. 418
References	p. 420
Index	p. 423
Table of Contents provided by Ingram. All Rights Reserved.

Lecture Notes in Physics

The Ads/CFT Correspondence

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Paperback

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