1. Strong coupling problems in condensed matter and the AdS/CFT correspondence HARVARD arXiv:0910.1139 Reviews: Talk online: sachdev.physics.harvard.edu arXiv:0901.4103

2. Frederik Denef, Harvard Sean Hartnoll, Harvard Christopher Herzog, Princeton Pavel Kovtun, Victoria Dam Son, Washington Frederik Denef, Harvard Sean Hartnoll, Harvard Christopher Herzog, Princeton Pavel Kovtun, Victoria Dam Son, Washington Max Metlitski, Harvard HARVARD

3. 1. Quantum-critical transport Collisionless-t0-hydrodynamic crossover of CFT3s 2. Exact solution from AdS/CFT 3. Quantum criticality of Fermi surfaces The genus expansion

4. 1. Quantum-critical transport Collisionless-t0-hydrodynamic crossover of CFT3s 2. Exact solution from AdS/CFT 3. Quantum criticality of Fermi surfaces The genus expansion

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6. M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature 415, 39 (2002). Superfluid-insulator transition

7. Cheng Chin James Franck institute Physics Department Chicago University Having your cake and seeing it too - Exploring quantum criticality and critical dynamics in ultracold atomic gases

8. Insulator (the vacuum) at large U

9. Excitations:

11. Excitations of the insulator:

13. CFT3

15. Classical vortices and wave oscillations of the condensate Dilute Boltzmann/Landau gas of particle and holes

16. CFT at T>0

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18. Quantum critical transport S. Sachdev, Quantum Phase Transitions, Cambridge (1999).

19. Quantum critical transport K. Damle and S. Sachdev, Phys. Rev. B 56, 8714 (1997).

20. Quantum critical transport P. Kovtun, D. T. Son, and A. Starinets, Phys. Rev. Lett. 94, 11601 (2005), 8714 (1997).

21. Quantum critical transport

24. Density correlations in CFTs at T >0

26. Conformal mapping of plane to cylinder with circumference 1/T

28. Density correlations in CFTs at T >0 No hydrodynamics in CFT2s.

29. Density correlations in CFTs at T >0

30. K. Damle and S. Sachdev, Phys. Rev. B 56, 8714 (1997).

31. Density correlations in CFTs at T >0 K. Damle and S. Sachdev, Phys. Rev. B 56, 8714 (1997).

32. 1. Quantum-critical transport Collisionless-t0-hydrodynamic crossover of CFT3s 2. Exact solution from AdS/CFT 3. Quantum criticality of Fermi surfaces The genus expansion

33. 1. Quantum-critical transport Collisionless-t0-hydrodynamic crossover of CFT3s 2. Exact solution from AdS/CFT 3. Quantum criticality of Fermi surfaces The genus expansion

45. P. Kovtun, C. Herzog, S. Sachdev, and D.T. Son, Phys. Rev. D 75, 085020 (2007) Collisionless to hydrodynamic crossover of SYM3

46. P. Kovtun, C. Herzog, S. Sachdev, and D.T. Son, Phys. Rev. D 75, 085020 (2007) Collisionless to hydrodynamic crossover of SYM3

47. Universal constants of SYM3 P. Kovtun, C. Herzog, S. Sachdev, and D.T. Son, Phys. Rev. D 75, 085020 (2007) C. Herzog, JHEP 0212, 026 (2002)

48. Electromagnetic self-duality

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51. Electromagnetic self-duality

53. 1. Quantum-critical transport Collisionless-t0-hydrodynamic crossover of CFT3s 2. Exact solution from AdS/CFT 3. Quantum criticality of Fermi surfaces The genus expansion

54. 1. Quantum-critical transport Collisionless-t0-hydrodynamic crossover of CFT3s 2. Exact solution from AdS/CFT 3. Quantum criticality of Fermi surfaces The genus expansion

55. Theory of quantum criticality in the cuprates

57. Nematic order in YBCO V. Hinkov, D. Haug, B. Fauqué, P. Bourges, Y. Sidis, A. Ivanov, C. Bernhard, C. T. Lin, and B. Keimer, Science 319, 597 (2008)

58. Nematic order in YBCO V. Hinkov, D. Haug, B. Fauqué, P. Bourges, Y. Sidis, A. Ivanov, C. Bernhard, C. T. Lin, and B. Keimer, Science 319, 597 (2008)

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60. “Large” Fermi surfaces in cuprates Hole states occupied Electron states occupied

61. Quantum criticality of Pomeranchuk instability x y

62. Electron Green’s function in Fermi liquid (T=0)

64. Quantum criticality of Pomeranchuk instability x y

65. x y

66. x y

68. Quantum critical

69. Quantum criticality of Pomeranchuk instability Quantum critical Classical d=2 Ising criticality

70. Quantum criticality of Pomeranchuk instability Quantum critical D=2+1 Ising criticality ?

71. Quantum criticality of Pomeranchuk instability

76. Hertz theory

77. Quantum criticality of Pomeranchuk instability Hertz theory

78. Quantum criticality of Pomeranchuk instability Sung-Sik Lee, Physical Review B 80, 165102 (2009)

79. Quantum criticality of Pomeranchuk instability A string theory for the Fermi surface ?

83. AdS 4 -Reissner-Nordstrom black hole

84. T. Faulkner, H. Liu, J. McGreevy, and D. Vegh, arXiv:0907.2694 F. Denef, S. Hartnoll, and S. Sachdev, arXiv:0908.1788 Examine free energy and Green’s function of a probe particle

85. Short time behavior depends upon conformal AdS 4 geometry near boundary T. Faulkner, H. Liu, J. McGreevy, and D. Vegh, arXiv:0907.2694 F. Denef, S. Hartnoll, and S. Sachdev, arXiv:0908.1788

86. Long time behavior depends upon near-horizon geometry of black hole T. Faulkner, H. Liu, J. McGreevy, and D. Vegh, arXiv:0907.2694 F. Denef, S. Hartnoll, and S. Sachdev, arXiv:0908.1788

87. Radial direction of gravity theory is measure of energy scale in CFT T. Faulkner, H. Liu, J. McGreevy, and D. Vegh, arXiv:0907.2694 F. Denef, S. Hartnoll, and S. Sachdev, arXiv:0908.1788

88. AdS 4 -Reissner-Nordstrom black hole

89. AdS 2 x R 2 near-horizon geometry

90. T. Faulkner, H. Liu, J. McGreevy, and D. Vegh, arXiv:0907.2694 Infrared physics of Fermi surface is linked to the near horizon AdS 2 geometry of Reissner-Nordstrom black hole

91. T. Faulkner, H. Liu, J. McGreevy, and D. Vegh, arXiv:0907.2694 AdS 4 Geometric interpretation of RG flow

92. T. Faulkner, H. Liu, J. McGreevy, and D. Vegh, arXiv:0907.2694 AdS 2 x R 2 Geometric interpretation of RG flow

93. Green’s function of a fermion T. Faulkner, H. Liu, J. McGreevy, and D. Vegh, arXiv:0907.2694 See also M. Cubrovic, J Zaanen, and K. Schalm, arXiv:0904.1993

94. Green’s function of a fermion T. Faulkner, H. Liu, J. McGreevy, and D. Vegh, arXiv:0907.2694 Similar to non-Fermi liquid theories of Fermi surfaces coupled to gauge fields, and at quantum critical points

95. General theory of finite temperature dynamics and transport near quantum critical points, with applications to antiferromagnets, graphene, and superconductors Conclusions

96. The AdS/CFT offers promise in providing a new understanding of strongly interacting quantum matter at non-zero density Conclusions