Non-relativistic AdS/CFT and the GCA

Abstract

We construct a non-relativistic limit of the AdS/CFT conjecture by taking, on the boundary side, a parametric group contraction of the relativistic conformal group. This leads to an algebra with the same number of generators called the Galilean Conformal Algebra (GCA). The GCA is to be contrasted with the more widely studied Schrodinger algebra which has fewer generators. The GCA, interestingly, can be given an infinite dimensional lift for any dimension of spacetime and this infinite algebra contains a Virasoro Kac-Moody sub-algebra. We comment briefly on potential realizations of this algebra in real-life systems. We also propose a somewhat unusual geometric structure for the bulk gravity dual to the GCA. This involves taking a Newton-Cartan like limit of Einstein's equations in anti de Sitter space which singles out an AdS2 comprising of the time and radial direction. The infinite dimensional GCA arises out of the contraction of the bulk Killing vectors and is identified with the (asymptotic) isometries of this Newton-Cartan structure.