AdS/CFT duality for non-relativistic field theory

Abstract

We formulate a correspondence between non-relativistic conformal field theories (NRCFTs) in d-1 spatial dimensions and gravitational theories in AdS d+2 backgrounds with one compactified lightlike direction. The breaking of the maximal SO(2,d+1) symmetry of AdS d+2 to the non-relativistic conformal group arises from boundary conditions on bulk fields, without the need to introduce non-vacuum sources of energy-momentum. As a check of the proposal, we use the gravitational theory to reproduce the NRCFT state-operator correspondence between scaling dimensions of primary operators and energy eigenstates of the non-relativistic system placed in an external harmonic potential. © SISSA 2009.