On AdS/CFT of Galilean Conformal Field Theories

TL;DR

This paper explores a new contraction of relativistic conformal algebra leading to Galilean conformal field theories and investigates their gravity duals via a Newton-Cartan limit of Einstein's equations, revealing connections to AdS spacetimes.

Contribution

It introduces a novel algebraic contraction of conformal symmetry and analyzes the corresponding gravity duals, extending the AdS/CFT correspondence to Galilean conformal field theories.

Findings

Infinite dimensional extensions for n=0,1 with Virasoro algebra

Finite algebra for n>1 containing so(2,n+1)

Gravity duals involve AdS_{n+2} spacetimes

Abstract

We study a new contraction of a d+1 dimensional relativistic conformal algebra where n+1 directions remain unchanged. For n=0,1 the resultant algebras admit infinite dimensional extension containing one and two copies of Virasoro algebra, respectively. For n> 1 the obtained algebra is finite dimensional containing an so(2,n+1) subalgebra. The gravity dual is provided by taking a Newton-Cartan like limit of the Einstein's equations of AdS space which singles out an AdS_{n+2} spacetime. The infinite dimensional extension of n=0,1 cases may be understood from the fact that the dual gravities contain AdS_2 and AdS_3 factor, respectively. We also explore how the AdS/CFT correspondence works for this case where we see that the main role is playing by AdS_{n+2} base geometry.