1. AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu

2. Particle theorists Sean Hartnoll, KITP Christopher Herzog, Princeton Pavel Kovtun, Victoria Dam Son, Washington Sean Hartnoll, KITP Christopher Herzog, Princeton Pavel Kovtun, Victoria Dam Son, Washington

3. Markus Mueller Geneva Markus Mueller Geneva Condensed matter theorists Cenke Xu Harvard Cenke Xu Harvard Yang Qi Harvard Yang Qi Harvard

4. Three foci of modern physics Quantum phase transitions

5. Three foci of modern physics Quantum phase transitions Many QPTs of correlated electrons in 2+1 dimensions are described by conformal field theories (CFTs)

6. Three foci of modern physics Quantum phase transitions Black holes

7. Three foci of modern physics Quantum phase transitions Black holes Bekenstein and Hawking originated the quantum theory, which has found fruition in string theory

8. Three foci of modern physics Quantum phase transitions Black holes Hydrodynamics

9. Three foci of modern physics Quantum phase transitions Black holes Hydrodynamics Universal description of fluids based upon conservation laws and positivity of entropy production

10. Three foci of modern physics Quantum phase transitions Black holes Hydrodynamics

11. Three foci of modern physics Quantum phase transitions Black holes Hydrodynamics Canonical problem in condensed matter: transport properties of a correlated electron system

12. Three foci of modern physics Quantum phase transitions Black holes Hydrodynamics Canonical problem in condensed matter: transport properties of a correlated electron system New insights and results from detour unifies disparate fields of physics

13. Three foci of modern physics Quantum phase transitions Black holes Hydrodynamics

14. Three foci of modern physics Quantum phase transitions Black holes Hydrodynamics Many QPTs of correlated electrons in 2+1 dimensions are described by conformal field theories (CFTs)

15. Three foci of modern physics Black holes Hydrodynamics Quantum phase transitions Many QPTs of correlated electrons in 2+1 dimensions are described by conformal field theories (CFTs)

16. Ground state has long-range Néel order Square lattice antiferromagnet

17. J J/ Weaken some bonds to induce spin entanglement in a new quantum phase

18. M. Matsumoto, C. Yasuda, S. Todo, and H. Takayama, Phys. Rev.B 65, 014407 (2002). Quantum critical point with non-local entanglement in spin wavefunction

19. CFT3

20. S. Wenzel and W. Janke, arXiv:0808.1418 M. Troyer, M. Imada, and K. Ueda, J. Phys. Soc. Japan (1997) Quantum Monte Carlo - critical exponents

21. Field-theoretic RG of CFT3 E. Vicari et al. S. Wenzel and W. Janke, arXiv:0808.1418 M. Troyer, M. Imada, and K. Ueda, J. Phys. Soc. Japan (1997)

22. TlCuCl 3

23. Pressure in TlCuCl 3

24. N. Cavadini, G. Heigold, W. Henggeler, A. Furrer, H.-U. Güdel, K. Krämer and H. Mutka, Phys. Rev. B 63 172414 (2001). “triplon” TlCuCl 3 at ambient pressure

25. Christian Ruegg, Bruce Normand, Masashige Matsumoto, Albert Furrer, Desmond McMorrow, Karl Kramer, Hans–Ulrich Gudel, Severian Gvasaliya, Hannu Mutka, and Martin Boehm, Phys. Rev. Lett. 100, 205701 (2008) TlCuCl 3 with varying pressure

26. Half-filled band  Mott insulator with spin S = 1/2 Triangular lattice of [Pd(dmit) 2 ] 2  frustrated quantum spin system X[Pd(dmit) 2 ] 2 Pd SC X Pd(dmit) 2 t’ t t Y. Shimizu, H. Akimoto, H. Tsujii, A. Tajima, and R. Kato, J. Phys.: Condens. Matter 19, 145240 (2007)

29. Anisotropic triangular lattice antiferromagnet Neel ground state for small J’/J Broken spin rotation symmetry

30. Anisotropic triangular lattice antiferromagnet

31. Magnetic Criticality T N (K) Neel order Me 4 P Me 4 As EtMe 3 As Et 2 Me 2 As Me 4 Sb Et 2 Me 2 P EtMe 3 Sb Y. Shimizu, H. Akimoto, H. Tsujii, A. Tajima, and R. Kato, J. Phys.: Condens. Matter 19, 145240 (2007) X[Pd(dmit) 2 ] 2 Et 2 Me 2 Sb (CO)

32. Anisotropic triangular lattice antiferromagnet Possible ground state for intermediate J’/J

33. Anisotropic triangular lattice antiferromagnet Possible ground state for intermediate J’/J Valence bond solid (VBS) Broken lattice space group symmetry

34. Anisotropic triangular lattice antiferromagnet Possible ground state for intermediate J’/J Valence bond solid (VBS) Broken lattice space group symmetry

35. Anisotropic triangular lattice antiferromagnet Possible ground state for intermediate J’/J Valence bond solid (VBS) Broken lattice space group symmetry

36. Anisotropic triangular lattice antiferromagnet Possible ground state for intermediate J’/J Valence bond solid (VBS) Broken lattice space group symmetry

37. Anisotropic triangular lattice antiferromagnet

38. Magnetic Criticality T N (K) Neel order Me 4 P Me 4 As EtMe 3 As Et 2 Me 2 As Me 4 Sb Et 2 Me 2 P EtMe 3 Sb Y. Shimizu, H. Akimoto, H. Tsujii, A. Tajima, and R. Kato, J. Phys.: Condens. Matter 19, 145240 (2007) X[Pd(dmit) 2 ] 2 Et 2 Me 2 Sb (CO)

39. Magnetic Criticality T N (K) Neel order Me 4 P Me 4 As EtMe 3 As Et 2 Me 2 As Me 4 Sb Et 2 Me 2 P EtMe 3 Sb EtMe 3 P Y. Shimizu, H. Akimoto, H. Tsujii, A. Tajima, and R. Kato, J. Phys.: Condens. Matter 19, 145240 (2007) X[Pd(dmit) 2 ] 2 Et 2 Me 2 Sb (CO) Spin gap Spin gap

40. Magnetic Criticality T N (K) Neel order Me 4 P Me 4 As EtMe 3 As Et 2 Me 2 As Me 4 Sb Et 2 Me 2 P EtMe 3 Sb EtMe 3 P Y. Shimizu, H. Akimoto, H. Tsujii, A. Tajima, and R. Kato, J. Phys.: Condens. Matter 19, 145240 (2007) X[Pd(dmit) 2 ] 2 Et 2 Me 2 Sb (CO) VBS order Spin gap Spin gap

41. M. Tamura, A. Nakao and R. Kato, J. Phys. Soc. Japan 75, 093701 (2006) Y. Shimizu, H. Akimoto, H. Tsujii, A. Tajima, and R. Kato, Phys. Rev. Lett. 99, 256403 (2007) Observation of a valence bond solid (VBS) in ETMe 3 P[Pd(dmit) 2 ] 2 Spin gap ~ 40 K J ~ 250 K X-ray scattering

42. Magnetic Criticality T N (K) Neel order Me 4 P Me 4 As EtMe 3 As Et 2 Me 2 As Me 4 Sb Et 2 Me 2 P EtMe 3 Sb EtMe 3 P Y. Shimizu, H. Akimoto, H. Tsujii, A. Tajima, and R. Kato, J. Phys.: Condens. Matter 19, 145240 (2007) X[Pd(dmit) 2 ] 2 Et 2 Me 2 Sb (CO) VBS order Spin gap Spin gap

43. Anisotropic triangular lattice antiferromagnet

44. Classical ground state for large J’/J Found in Cs 2 CuCl 4

45. Anisotropic triangular lattice antiferromagnet

47. Spin liquid obtained in a generalized spin model with S=1/2 per unit cell = P. Fazekas and P. W. Anderson, Philos. Mag. 30, 23 (1974). Triangular lattice antiferromagnet

48. P. Fazekas and P. W. Anderson, Philos. Mag. 30, 23 (1974). Spin liquid obtained in a generalized spin model with S=1/2 per unit cell = Triangular lattice antiferromagnet

49. P. Fazekas and P. W. Anderson, Philos. Mag. 30, 23 (1974). Spin liquid obtained in a generalized spin model with S=1/2 per unit cell = Triangular lattice antiferromagnet

50. P. Fazekas and P. W. Anderson, Philos. Mag. 30, 23 (1974). Spin liquid obtained in a generalized spin model with S=1/2 per unit cell = Triangular lattice antiferromagnet

51. P. Fazekas and P. W. Anderson, Philos. Mag. 30, 23 (1974). Spin liquid obtained in a generalized spin model with S=1/2 per unit cell = Triangular lattice antiferromagnet

52. P. Fazekas and P. W. Anderson, Philos. Mag. 30, 23 (1974). Spin liquid obtained in a generalized spin model with S=1/2 per unit cell = Triangular lattice antiferromagnet

53. Excitations of the Z 2 Spin liquid = A spinon

54. Excitations of the Z 2 Spin liquid = A spinon

55. Excitations of the Z 2 Spin liquid = A spinon

56. Excitations of the Z 2 Spin liquid = A spinon

57. Excitations of the Z 2 Spin liquid A spinon

58. Excitations of the Z 2 Spin liquid A spinon

59. Excitations of the Z 2 Spin liquid A vison N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)

60. = Excitations of the Z 2 Spin liquid A vison N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)

61. = Excitations of the Z 2 Spin liquid A vison N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)

62. = Excitations of the Z 2 Spin liquid A vison N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)

63. = Excitations of the Z 2 Spin liquid A vison N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)

64. = Excitations of the Z 2 Spin liquid A vison N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)

65. = Excitations of the Z 2 Spin liquid A vison N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)

66. A Simple Toy Model (A. Kitaev, 1997)‏ Spins S α living on the links of a square lattice: − Hence, F p 's and A i 's form a set of conserved quantities.

67. A Simple Toy Model (A. Kitaev, 1997)‏ Spins S α living on the links of a square lattice: − Hence, F p 's and A i 's form a set of conserved quantities.

68. A Simple Toy Model (A. Kitaev, 1997)‏ Spins S α living on the links of a square lattice: − Hence, F p 's and A i 's form a set of conserved quantities.

69. A Simple Toy Model (A. Kitaev, 1997)‏ Spins S α living on the links of a square lattice: − Hence, F p 's and A i 's form a set of conserved quantities.

70. A Simple Toy Model (A. Kitaev, 1997)‏ Spins S α living on the links of a square lattice: − Hence, F p 's and A i 's form a set of conserved quantities.

71. A Simple Toy Model (A. Kitaev, 1997)‏ Spins S α living on the links of a square lattice: − Hence, F p 's and A i 's form a set of conserved quantities.

72. A Simple Toy Model (A. Kitaev, 1997)‏ Spins S α living on the links of a square lattice: − Hence, F p 's and A i 's form a set of conserved quantities.

73. A Simple Toy Model (A. Kitaev, 1997)‏ Spins S α living on the links of a square lattice: − Hence, F p 's and A i 's form a set of conserved quantities.

74. A Simple Toy Model (A. Kitaev, 1997)‏ Spins S α living on the links of a square lattice: − Hence, F p 's and A i 's form a set of conserved quantities.

75. A Simple Toy Model (A. Kitaev, 1997)‏ Spins S α living on the links of a square lattice: − Hence, F p 's and A i 's form a set of conserved quantities.

76. A Simple Toy Model (A. Kitaev, 1997)‏ Spins S α living on the links of a square lattice: − Hence, F p 's and A i 's form a set of conserved quantities.

77. Properties of the Ground State Ground state: all A i =1, F p =1 Pictorial representation: color each link with an up-spin. A i =1 : closed loops. F p =1 : every plaquette is an equal-amplitude superposition of inverse images. The GS wavefunction takes the same value on configurations connected by these operations. It does not depend on the geometry of the configurations, only on their topology.

78. Properties of Excitations “Electric” particle, or A i = – 1 – endpoint of a line “Magnetic particle”, or vortex: F p = – 1 – a “flip” of this plaquette changes the sign of a given term in the superposition. Charges and vortices interact via topological Aharonov-Bohm interactions.

79. Properties of Excitations “Electric” particle, or A i = – 1 – endpoint of a line (a “spinon”) “Magnetic particle”, or vortex: F p = – 1 – a “flip” of this plaquette changes the sign of a given term in the superposition. Charges and vortices interact via topological Aharonov-Bohm interactions.

80. Properties of Excitations “Electric” particle, or A i = – 1 – endpoint of a line (a “spinon”) “Magnetic particle”, or vortex: F p = – 1 – a “flip” of this plaquette changes the sign of a given term in the superposition (a “vison”). Charges and vortices interact via topological Aharonov-Bohm interactions.

81. Properties of Excitations “Electric” particle, or A i = – 1 – endpoint of a line (a “spinon”) “Magnetic particle”, or vortex: F p = – 1 – a “flip” of this plaquette changes the sign of a given term in the superposition (a “vison”). Charges and vortices interact via topological Aharonov-Bohm interactions. Spinons and visons are mutual semions

82. Mutual Chern-Simons Theory Cenke Xu and S. Sachdev, arXiv:0811.1220

84. N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991) T. Senthil, A. Vishwanath, L. Balents, S. Sachdev and M.P.A. Fisher, Science 303, 1490 (2004). Cenke Xu and S. Sachdev, arXiv:0811.1220 Theoretical global phase diagram

85. N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991) T. Senthil, A. Vishwanath, L. Balents, S. Sachdev and M.P.A. Fisher, Science 303, 1490 (2004). Cenke Xu and S. Sachdev, arXiv:0811.1220 Theoretical global phase diagram CFTs

86. Magnetic Criticality T N (K) Neel order Me 4 P Me 4 As EtMe 3 As Et 2 Me 2 As Me 4 Sb Et 2 Me 2 P EtMe 3 Sb EtMe 3 P Y. Shimizu, H. Akimoto, H. Tsujii, A. Tajima, and R. Kato, J. Phys.: Condens. Matter 19, 145240 (2007) X[Pd(dmit) 2 ] 2 Et 2 Me 2 Sb (CO) Spin gap Spin gap VBS order

87. Magnetic Criticality T N (K) Neel order Me 4 P Me 4 As EtMe 3 As Et 2 Me 2 As Me 4 Sb Et 2 Me 2 P EtMe 3 Sb EtMe 3 P Y. Shimizu, H. Akimoto, H. Tsujii, A. Tajima, and R. Kato, J. Phys.: Condens. Matter 19, 145240 (2007) X[Pd(dmit) 2 ] 2 Et 2 Me 2 Sb (CO) VBS order Spin gap Spin gap Quantum criticality described by CFT Quantum criticality described by CFT

88. From quantum antiferromagnets to string theory

89. Three foci of modern physics Quantum phase transitions Black holes Hydrodynamics

90. Black holes Three foci of modern physics Quantum phase transitions Hydrodynamics Canonical problem in condensed matter: transport properties of a correlated electron system

91. Black holes Three foci of modern physics Quantum phase transitions Hydrodynamics Canonical problem in condensed matter: transport properties of a correlated electron system

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

94. CFT3

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

97. CFT at T>0

98. D. B. Haviland, Y. Liu, and A. M. Goldman, Phys. Rev. Lett. 62, 2180 (1989) Resistivity of Bi films M. P. A. Fisher, Phys. Rev. Lett. 65, 923 (1990)

99. Density correlations in CFTs at T >0

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

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

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

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

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

105. Three foci of modern physics Quantum phase transitions Black holes Hydrodynamics

106. Quantum phase transitions Three foci of modern physics Black holes New insights and results from detour unifies disparate fields of physics Canonical problem in condensed matter: transport properties of a correlated electron system

107. Hydrodynamics Quantum phase transitions Three foci of modern physics Black holes New insights and results from detour unifies disparate fields of physics Canonical problem in condensed matter: transport properties of a correlated electron system 1

108. Hydrodynamics of quantum critical systems 1. Use quantum field theory + quantum transport equations + classical hydrodynamics Uses physical model but strong-coupling makes explicit solution difficult 2. Solve Einstein-Maxwell equations in the background of a black hole in AdS space Yields hydrodynamic relations which apply to general classes of quantum critical systems. First exact numerical results for transport co-efficients (for supersymmetric systems).

109. Hydrodynamics Quantum phase transitions Three foci of modern physics Black holes New insights and results from detour unifies disparate fields of physics Canonical problem in condensed matter: transport properties of a correlated electron system 1

110. Hydrodynamics Quantum phase transitions Three foci of modern physics Black holes New insights and results from detour unifies disparate fields of physics Canonical problem in condensed matter: transport properties of a correlated electron system 1 2

111. Hydrodynamics of quantum critical systems 1. Use quantum field theory + quantum transport equations + classical hydrodynamics Uses physical model but strong-coupling makes explicit solution difficult 2. Solve Einstein-Maxwell equations in the background of a black hole in AdS space Yields hydrodynamic relations which apply to general classes of quantum critical systems. First exact numerical results for transport co-efficients (for supersymmetric systems).

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

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

114. The cuprate superconductors

115. Proximity to an insulator at 12.5% hole concentration

116. Thermoelectric measurements CFT3 ? Cuprates STM image of Y. Kohsaka et al., Science 315, 1380 (2007).

118. For experimental applications, we must move away from the ideal CFT e.g. A chemical potential   A magnetic field B CFT

121. S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B 76 144502 (2007)

122. Conservation laws/equations of motion S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B 76 144502 (2007)

123. Constitutive relations which follow from Lorentz transformation to moving frame S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B 76 144502 (2007)

124. Single dissipative term allowed by requirement of positive entropy production. There is only one independent transport co-efficient S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B 76 144502 (2007)

125. For experimental applications, we must move away from the ideal CFT e.g. A chemical potential   A magnetic field B CFT

126. For experimental applications, we must move away from the ideal CFT e.g. CFT A chemical potential   A magnetic field B An impurity scattering rate 1/  imp (its T dependence follows from scaling arguments)

127. For experimental applications, we must move away from the ideal CFT e.g. A chemical potential   A magnetic field B An impurity scattering rate 1/  imp (its T dependence follows from scaling arguments) CFT

128. S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B 76 144502 (2007)

130. Solve initial value problem and relate results to response functions (Kadanoff+Martin)

131. From these relations, we obtained results for the transport co-efficients, expressed in terms of a “cyclotron” frequency and damping: S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B 76 144502 (2007)

132. From these relations, we obtained results for the transport co-efficients, expressed in terms of a “cyclotron” frequency and damping: S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B 76 144502 (2007)

134. From these relations, we obtained results for the transport co-efficients, expressed in terms of a “cyclotron” frequency and damping: S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B 76 144502 (2007)

135. From these relations, we obtained results for the transport co-efficients, expressed in terms of a “cyclotron” frequency and damping: S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B 76 144502 (2007)

136. From these relations, we obtained results for the transport co-efficients, expressed in terms of a “cyclotron” frequency and damping: S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B 76 144502 (2007)

137. Nernst experiment Vortices move in a temperature gradient Phase slip generates Josephson voltage 2eV J = 2  h n V E J = B x v H eyey HmHm Nernst signal e y = E y /| T |

138. From these relations, we obtained results for the transport co-efficients, expressed in terms of a “cyclotron” frequency and damping: S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B 76 144502 (2007)

139. To the solvable supersymmetric, Yang-Mills theory CFT, we add A chemical potential   A magnetic field B After the AdS/CFT mapping, we obtain the Einstein-Maxwell theory of a black hole with An electric charge  A magnetic charge The exact results are found to be in precise accord with all hydrodynamic results presented earlier S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B 76 144502 (2007) Exact Results

140. Y. Wang, L. Li, and N. P. Ong, Phys. Rev. B 73, 024510 (2006). Theory for LSCO Experiments

143. Doubled U(1) Chern-Simons theory is useful for building a global phase diagram of two- dimensional quantum antiferromagnets. The same theory with a U(N) gauge group and extended supersymmetry describes M theory on AdS 4 Exact solutions via black hole mapping have yielded first exact results for transport co- efficients in interacting many-body systems, and were valuable in determining general structure of hydrodynamics. Theory of Nernst effect near the superfluid- insulator transition, and connection to cuprates. Doubled U(1) Chern-Simons theory is useful for building a global phase diagram of two- dimensional quantum antiferromagnets. The same theory with a U(N) gauge group and extended supersymmetry describes M theory on AdS 4 Exact solutions via black hole mapping have yielded first exact results for transport co- efficients in interacting many-body systems, and were valuable in determining general structure of hydrodynamics. Theory of Nernst effect near the superfluid- insulator transition, and connection to cuprates. Conclusions

144. Doubled U(1) Chern-Simons theory is useful for building a global phase diagram of two- dimensional quantum antiferromagnets. The same theory with a U(N) gauge group and extended supersymmetry describes M theory on AdS 4 Exact solutions via black hole mapping have yielded first exact results for transport co- efficients in interacting many-body systems, and were valuable in determining general structure of hydrodynamics. Theory of Nernst effect near the superfluid- insulator transition, and connection to cuprates. Doubled U(1) Chern-Simons theory is useful for building a global phase diagram of two- dimensional quantum antiferromagnets. The same theory with a U(N) gauge group and extended supersymmetry describes M theory on AdS 4 Exact solutions via black hole mapping have yielded first exact results for transport co- efficients in interacting many-body systems, and were valuable in determining general structure of hydrodynamics. Theory of Nernst effect near the superfluid- insulator transition, and connection to cuprates. Conclusions

145. Doubled U(1) Chern-Simons theory is useful for building a global phase diagram of two- dimensional quantum antiferromagnets. The same theory with a U(N) gauge group and extended supersymmetry describes M theory on AdS 4 Exact solutions via black hole mapping have yielded first exact results for transport co- efficients in interacting many-body systems, and were valuable in determining general structure of hydrodynamics. Theory of Nernst effect near the superfluid- insulator transition, and connection to cuprates. Doubled U(1) Chern-Simons theory is useful for building a global phase diagram of two- dimensional quantum antiferromagnets. The same theory with a U(N) gauge group and extended supersymmetry describes M theory on AdS 4 Exact solutions via black hole mapping have yielded first exact results for transport co- efficients in interacting many-body systems, and were valuable in determining general structure of hydrodynamics. Theory of Nernst effect near the superfluid- insulator transition, and connection to cuprates. Conclusions