Galilean Conformal Algebras and AdS/CFT

TL;DR

This paper explores a new non-relativistic conformal symmetry called Galilean Conformal Algebra, its infinite-dimensional extension, and proposes a novel gravity dual involving a Newton-Cartan limit of AdS space.

Contribution

It introduces the Galilean Conformal Algebra, its infinite extension with Virasoro symmetry, and a new geometric bulk dual based on a Newton-Cartan limit of AdS.

Findings

Galilean Conformal Algebra admits an infinite dimensional extension.

The extended algebra contains a Virasoro-Kac-Moody subalgebra.

A proposed gravity dual involves a Newton-Cartan limit of Einstein's equations.

Abstract

Non-relativistic versions of the AdS/CFT conjecture have recently been investigated in some detail. These have primarily been in the context of the Schrodinger symmetry group. Here we initiate a study based on a {\it different} non-relativistic conformal symmetry: one obtained by a parametric contraction of the relativistic conformal group. The resulting Galilean conformal symmetry has the same number of generators as the relativistic symmetry group and thus is different from the Schrodinger group (which has fewer). One of the interesting features of the Galilean Conformal Algebra is that it admits an extension to an {\it infinite} dimensional symmetry algebra (which can potentially be dynamically realised). The latter contains a Virasoro-Kac-Moody subalgebra. We comment on realisations of this extended symmetry in a boundary field theory. We also propose a somewhat unusual geometric structure for the bulk gravity dual to any realisation of this symmetry. This involves taking a Newton-Cartan like limit of Einstein's equations in anti de Sitter space which singles out an $AdS_2$ comprising of the time and radial direction. The infinite dimensional Virasoro extension is identified with the asymptotic isometries of this $AdS_2$.