Holography and condensed matter

This is a short review of recent developments in the application of AdS/CFT methods to some condensed matter problems. In particular we present the holographic description of a local quantum critical state, related to (non)-Fermi liquids and the strange metal, that appears in large N CFTs with a gravity dual at finite density and zero temperature, and explore its properties by probing it with fermionic operators. Further we discuss possible bosonic and fermionic instabilities, leading to s-, p- or d-wave holographic superconductors and "electron stars". Finally we present a realization of local quantum criticality via an impurity problem.Comment: 11 pages, 4 figures; Contribution to the proceedings of the "XVII European Workshop on String Theory 2011", Padova, Italy, 5-9 September 2011; v2: ref adde