Condensed matter and AdS/CFT Subir Sachdev Lectures at the 5th Aegean summer school, “From gravity to thermal gauge the- ories: the AdS/CFT correspondence”, Adamas, Milos Island, Greece, September 21-26, 2009, and the De Sitter Lecture Series in Theoretical Physics 2009, University of Groningen, November 16-20, 2009. Abstract I review two classes of strong coupling problems in condensed matter physics, and describe insights gained by application of the AdS/CFT correspon- dence. The first class concerns non-zero temperature dynamics and transport in the vicinity of quantum critical points described by relativistic field theories. I de- scribe how relativistic structures arise in models of physical interest, present re- sults for their quantum critical crossover functions and magneto-thermoelectric hy- drodynamics. The second class concerns symmetry breaking transitions of two- dimensional systems in the presence of gapless electronic excitations at isolated points or along lines (i.e. Fermi surfaces) in the Brillouin zone. I describe the scal- ing structure of a recent theory of the Ising-nematic transition in metals, and discuss its possible connection to theories of Fermi surfaces obtained from simple AdS du- als. arXiv:1002.2947v1 [hep-th] 16 Feb 2010 Subir Sachdev Department of Physics, Harvard University, Cambridge MA 02138, e-mail:
[email protected] 1 2 Subir Sachdev 1 Introduction The past couple of decades have seen vigorous theoretical activity on the quantum phases and phase transitions of correlated electron systems in two spatial dimen- sions. Much of this work has been motivated by the cuprate superconductors, but the list of interesting materials continues to increase unabated [1].