1. Quantum-critical transport

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1. Quantum-critical transport
Collisionless-t0-hydrodynamic crossover of
CFT3s 2. Exact solution from AdS/CFT
Constraints from duality relations 3. Quantum
criticality of Dirac fermions Vector
1/N expansion 4. Quantum criticality of Fermi
surfaces The genus expansion
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1. Quantum-critical transport
Collisionless-t0-hydrodynamic crossover of
CFT3s 2. Exact solution from AdS/CFT
Constraints from duality relations 3. Quantum
criticality of Dirac fermions Vector
1/N expansion 4. Quantum criticality of Fermi
surfaces The genus expansion
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The Superfluid-Insulator transition
Boson Hubbard model
M.P. A. Fisher, P.B. Weichmann, G. Grinstein,
and D.S. Fisher, Phys. Rev. B 40, 546 (1989).
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Superfluid-insulator transition
M. Greiner, O. Mandel, T. Esslinger, T. W.
Hänsch, and I. Bloch, Nature 415, 39 (2002).
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Insulator (the vacuum) at large U
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Excitations
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Excitations
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Excitations of the insulator
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CFT3
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Classical vortices and wave oscillations of the
condensate
Dilute Boltzmann/Landau gas of particle and holes
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CFT at Tgt0
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Resistivity of Bi films
D. B. Haviland, Y. Liu, and A. M. Goldman, Phys.
Rev. Lett. 62, 2180 (1989)
M. P. A. Fisher, Phys. Rev. Lett. 65, 923 (1990)
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Quantum critical transport
S. Sachdev, Quantum Phase Transitions, Cambridge
(1999).
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Quantum critical transport
K. Damle and S. Sachdev, Phys. Rev. B 56, 8714
(1997).
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Quantum critical transport
P. Kovtun, D. T. Son, and A. Starinets, Phys.
Rev. Lett. 94, 11601 (2005) , 8714 (1997).
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Quantum critical transport
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Quantum critical transport
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Quantum critical transport
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Density correlations in CFTs at T gt0
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Conformal mapping of plane to cylinder with
circumference 1/T
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Conformal mapping of plane to cylinder with
circumference 1/T
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Density correlations in CFTs at T gt0
No hydrodynamics in CFT2s.
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Density correlations in CFTs at T gt0
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Density correlations in CFTs at T gt0
K. Damle and S. Sachdev, Phys. Rev. B 56, 8714
(1997).
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Density correlations in CFTs at T gt0
K. Damle and S. Sachdev, Phys. Rev. B 56, 8714
(1997).
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1. Quantum-critical transport
Collisionless-t0-hydrodynamic crossover of
CFT3s 2. Exact solution from AdS/CFT
Constraints from duality relations 3. Quantum
criticality of Dirac fermions Vector
1/N expansion 4. Quantum criticality of Fermi
surfaces The genus expansion
32
1. Quantum-critical transport
Collisionless-t0-hydrodynamic crossover of
CFT3s 2. Exact solution from AdS/CFT
Constraints from duality relations 3. Quantum
criticality of Dirac fermions Vector
1/N expansion 4. Quantum criticality of Fermi
surfaces The genus expansion
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Collisionless to hydrodynamic crossover of SYM3
P. Kovtun, C. Herzog, S. Sachdev, and D.T. Son,
Phys. Rev. D 75, 085020 (2007)
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Collisionless to hydrodynamic crossover of SYM3
P. Kovtun, C. Herzog, S. Sachdev, and D.T. Son,
Phys. Rev. D 75, 085020 (2007)
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Universal constants of SYM3
C. Herzog, JHEP 0212, 026 (2002)
P. Kovtun, C. Herzog, S. Sachdev, and D.T. Son,
Phys. Rev. D 75, 085020 (2007)
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Electromagnetic self-duality
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K a universal number analogous to the level
number of the Kac-Moody algebra in 11 dimensions
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C. Dasgupta and B.I. Halperin, Phys. Rev. Lett.
47, 1556 (1981)
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C. Dasgupta and B.I. Halperin, Phys. Rev. Lett.
47, 1556 (1981)
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C. Herzog, P. Kovtun, S. Sachdev, and D.T. Son,
hep-th/0701036
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The self-duality of the 4D abelian gauge fields
leads to
C. Herzog, P. Kovtun, S. Sachdev, and D.T. Son,
hep-th/0701036
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The self-duality of the 4D abelian gauge fields
leads to
C. Herzog, P. Kovtun, S. Sachdev, and D.T. Son,
hep-th/0701036
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Electromagnetic self-duality
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1. Quantum-critical transport
Collisionless-t0-hydrodynamic crossover of
CFT3s 2. Exact solution from AdS/CFT
Constraints from duality relations 3. Quantum
criticality of Dirac fermions Vector
1/N expansion 4. Quantum criticality of Fermi
surfaces The genus expansion
48
1. Quantum-critical transport
Collisionless-t0-hydrodynamic crossover of
CFT3s 2. Exact solution from AdS/CFT
Constraints from duality relations 3. Quantum
criticality of Dirac fermions Vector
1/N expansion 4. Quantum criticality of Fermi
surfaces The genus expansion
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d-wave superconductivity in cuprates
Electron states occupied
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d-wave superconductivity in cuprates
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d-wave superconductivity in cuprates
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d-wave superconductivity in cuprates
4 two-component Dirac fermions
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d-wave superconductivity in cuprates
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Time-reversal symmetry breaking
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Lattice rotation symmetry breaking
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M. Vojta, Y. Zhang, and S. Sachdev, Phys. Rev.
Lett. 85, 4940 (2000) E.-A. Kim, M. J. Lawler, P.
Oreto, S. Sachdev, E. Fradkin, S.A. Kivelson,
Phys. Rev. B 77, 184514 (2008).
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Ising order and Dirac fermions couple via a
Yukawa term.
Nematic ordering
Time reversal symmetry breaking
M. Vojta, Y. Zhang, and S. Sachdev, Physical
Review Letters 85, 4940 (2000)
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Ising order and Dirac fermions couple via a
Yukawa term.
Nematic ordering
Time reversal symmetry breaking
M. Vojta, Y. Zhang, and S. Sachdev, Physical
Review Letters 85, 4940 (2000)
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Expansion in number of fermion spin components Nf
Integrating out the fermions yields an effective
action for the scalar order parameter
Y. Huh and S. Sachdev, Physical Review B 78,
064512 (2008).
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1. Quantum-critical transport
Collisionless-t0-hydrodynamic crossover of
CFT3s 2. Exact solution from AdS/CFT
Constraints from duality relations 3. Quantum
criticality of Dirac fermions Vector
1/N expansion 4. Quantum criticality of Fermi
surfaces The genus expansion
62
1. Quantum-critical transport
Collisionless-t0-hydrodynamic crossover of
CFT3s 2. Exact solution from AdS/CFT
Constraints from duality relations 3. Quantum
criticality of Dirac fermions Vector
1/N expansion 4. Quantum criticality of Fermi
surfaces The genus expansion
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Quantum criticality of Pomeranchuk instability
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Electron Greens function in Fermi liquid (T0)
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Electron Greens function in Fermi liquid (T0)
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Quantum criticality of Pomeranchuk instability
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Quantum criticality of Pomeranchuk instability
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Quantum criticality of Pomeranchuk instability
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Quantum criticality of Pomeranchuk instability
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Quantum criticality of Pomeranchuk instability
Quantum critical
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Quantum criticality of Pomeranchuk instability
Quantum critical
Classical d2 Ising criticality
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Quantum criticality of Pomeranchuk instability
Quantum critical
D21 Ising criticality ?
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Quantum criticality of Pomeranchuk instability
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Quantum criticality of Pomeranchuk instability
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Quantum criticality of Pomeranchuk instability
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Quantum criticality of Pomeranchuk instability
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Quantum criticality of Pomeranchuk instability
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Quantum criticality of Pomeranchuk instability
Hertz theory
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Quantum criticality of Pomeranchuk instability
Sung-Sik Lee, Physical Review B 80, 165102 (2009)
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Quantum criticality of Pomeranchuk instability
A string theory for the Fermi surface ?
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Greens function of a fermion
T. Faulkner, H. Liu, J. McGreevy, and D. Vegh,
arXiv0907.2694
See also M. Cubrovic, J Zaanen, and K. Schalm,
arXiv0904.1993
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Greens function of a fermion
T. Faulkner, H. Liu, J. McGreevy, and D. Vegh,
arXiv0907.2694
Similar to non-Fermi liquid theories of Fermi
surfaces coupled to gauge fields, and at quantum
critical points
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Free energy from gravity theory
F. Denef, S. Hartnoll, and S. Sachdev,
arXiv0908.1788
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Conclusions
General theory of finite temperature dynamics
and transport near quantum critical points, with
applications to antiferromagnets, graphene, and
superconductors
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Conclusions
The AdS/CFT offers promise in providing a new
understanding of strongly interacting quantum
matter at non-zero density