Preface ........................................................ ix
1 Introduction ................................................. 1
1.1 A tour guide of holographiс matter ...................... 1
1.2 The AdS/CFT correspondence: unifying the theories of
physics ................................................. 3
1.3 AdS/CFT, the gеomеtrisation of the renormalisation
group and the quantum critical state .................... 6
1.4 Holographic duality and the nature of matter ........... 18
1.5 Holography, condensed matter physics and quantum
information ............................................ 27
2 Condensed matter: the charted territory ..................... 32
2.1 Quantum field theory in condensed matter: the
fluctuating order of bosons ............................ 34
2.2 Quantum matter: when entanglement becomes macroscopic .. 51
2.3 The remarkable Fermi liquid ............................ 57
2.4 The mean-field instabilities of the fermion system:
BCS and beyond ......................................... 64
2.5 The Hertz-Millis model and the critical Fermi surface .. 69
3 Condensed matter: the challenges ............................ 73
3.1 The repertoire of strongly correlated electron models .. 76
3.2 Mottness, non-Fermi liquids and RVB superconductivity .. 79
3.3 Unconventional superconductivity by weak repulsive
interactions ........................................... 88
3.4 Numerical machinery I: the density-matrix
renormalisation group and tensor-product states ........ 90
3.5 Numerical machinery II: infinitely many dimensions
and the dynamical mean-field theory .................... 92
3.6 Quantum matter in the laboratory ....................... 94
4 Large-TV field theories for holography and condensed
matter ..................................................... 105
4.1 A short history of the holographic principle, black
holes, string theory and the origins of the AdS/CFT
correspondence ........................................ 106
4.2 Yang-Mills as a matrix field theory and the ultimate
mean field at large-N ................................. 118
4.3 The master formulation of large-/V matrix models and
string theory ......................................... 130
4.4 The AdS/CFT correspondence is a field-theory/gravity
duality ............................................... 139
5 The AdS/CFT correspondence as computational device: the
dictionary ................................................. 151
5.1 The GKPW rule in action: computing correlation
functions ............................................. 154
5.2 Correlations, scaling and RG flows .................... 165
5.3 The identification of symmetries and the dictionary
table ................................................. 172
6 Finite-temperature magic: black holes and holographic
thermodynamics ............................................. 176
6.1 Black holes in the bulk and finite temperature in the
boundary .............................................. 178
6.2 Holographic thermodynamics: the Hawking-Page
transition ............................................ 193
6.3 A brief introduction to AdS/QCD ....................... 205
6.4 The GKPW rule at finite temperature: thermal
correlation functions and the Schwinger-Keldysh
formalism ............................................. 213
7 Holographic hydrodynamics .................................. 222
7.1 Quantum criticality and the minimal viscosity ......... 226
7.2 Deriving the Navier-Stokes fluid from the bulk
dynamical gravity ..................................... 238
7.3 The conductivity: conserved currents as photons in
the bulk .............................................. 243
7.4 Hydrodynamics and quantum anomalies ................... 253
8 Finite density: the Reissner-Nordstrцm black hole and
strange metals ............................................. 259
8.1 The Reissner-Nordstrцm strange metal .................. 261
8.2 The AdS2 near-horizon geometry and the emergent
local quantum criticality ............................. 267
8.3 The zero sound and conductivity of the RN metal in
the Galilean continuum ................................ 271
8.4 The scaling atlas of emergent holographic quantum
critical phases ....................................... 281
9 Holographie photoemission and the RN metal: the fermions
as probes .................................................. 291
9.1 The holographie encoding of fermions .................. 294
9.2 The discovery of the holographie Fermi surfaces ....... 304
9.3 Computing fermion spectral functions: Schrцdinger
potentials and the matching method .................... 312
9.4 The physics of the holographic fermions: confinement,
semi-holography and black-hole stability .............. 323
10 Holographic superconductivity .............................. 328
10.1 The black hole in AdS with scalar hair ................ 330
10.2 The phenomenology of holographic superconductivity .... 340
10.3 Observing the origin of Tc: the pair susceptibility
of the strange metal .................................. 355
10.4 The phase diagram of holographic superconductivity .... 362
10.5 The zero-temperature states of holographic
superconductors ....................................... 368
11 Holographic Fermi liquids: the stable Fermi liquid and
the electron star as holographic dual ...................... 377
11.1 The cohesive Landau Fermi liquid from hard-wall
holography ............................................ 381
11.2 The electron star as the dual of holographic
fermions .............................................. 390
11.3 The landscape of holographic Fermi liquids: radial
re-quantisation and instabilities ..................... 403
12 Breaking translational invariance .......................... 417
12.1 Transport and un-particle physics: the memory-matrix
formalism ............................................. 420
12.2 Periodic potentials in holographic superconductors
and the optical conductivity .......................... 432
12.3 Lattice potentials and the fermion spectral
functions of the Reissner-Nordström metal ............. 437
12.4 Unidirectional potentials becoming strong:
Bianchi VII geometry and the quantum smectic .......... 442
12.5 The dual of translational-symmetry breaking as
gravity with a mass ................................... 452
12.6 Holographic crystallisation: the spontaneous
breaking of translational symmetry .................... 463
13 AdS/CMT from the top down .................................. 470
13.1 Top-down AdS/CMT models from supergravity ............. 472
13.2 Probe-brane holography from Dp/Dg-brane
intersections ......................................... 483
14 Outlook: holography and quantum matter ..................... 504
14.1 The UHOs: the unidentified holographic objects ........ 505
14.2 Is holographic matter extreme quantum matter? ......... 511
14.3 The final message for condensed matter ................ 540
References .................................................... 543
Index ......................................................... 570
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