Applications of the AdS/CMT correspondence

Abstract

The AdS/CFT correspondence relates a gravitational theory in $AdS_{d+1}$ to a conformal field theory on its flat d-dimensional boundary, anda quasi-phenomenological approach was used to apply it to condensed matter systems. An abelian reduction of the ABJM model can be used to betterdefine the duality and one can study the relation between the resulting LG model and the original ABJM model. Theories with scalars around thehorizon of charged AdS black holes superconduct and have interesting transport properties. The horizon of $AdS_4$ black holes can be mapped toa fluid and one can study this correspondence for the case of the duality to the ABJM model. We will also study the possibility of obtaining2+1 dimensional Lifshitz points and points with Schr\"{o}dinger symmetry from limits of gravity duals.