On AdS/CFT of Galilean Conformal Field Theories

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.