High Energy Theory Seminar

(Based on arXiv:0902.1385, 0903.4543, 0912.1090) Non-relativistic versions of the AdS/CFT correspondence has received a lot of recent attention, much of which has been directed to systems with Schrodinger symmetry, the symmetry of free Schrodinger equations. In this talk, we outline a different non-relativistic version of AdS/CFT based on a systematic group contraction procedure. Taking this limit on the relativistic conformal algebra of the boundary theory, we get an algebra which we call the Galilean Conformal Algebra (GCA). The GCA has the interesting feature that it can be given an infinite dimensional lift for any space-time dimensions. On a more practical front, the GCA turns out to be the symmetry algebra of equations of non-relativistic hydrodynamics. We then look at the representations and correlation functions of the GCA and find novel structures for the two and three point functions from the finite algebra. The case of two dimensions is instructive because here the relativistic algebra becomes infinite dimensional. We find a simple relation between the two copies of the Virasoro algebra and the infinite GCA and go on to describe other features of the GCA in 2d. The bulk dual of the GCA is proposed to be a novel Newton-Cartan like $AdS_2 \times R^d$. The GCA in the bulk is realized by contraction of the Killing vectors and is interpreted as the asymptotic isometry of the above structure.