On AdS/CFT of Galilean Conformal Field Theories

TL;DR

This paper introduces a semi-Galilean contraction of the relativistic conformal algebra in $d+1$ dimensions that preserves $n+1$ directions and analyzes its holographic dual. For $n=0,1$ the symmetry algebra acquires infinite-dimensional Virasoro extensions due to base geometries $AdS_2$ or $AdS_3$, while for $n\ge 2$ the algebra remains finite with an $AdS_{n+2}$ base governing the gravity dual; the dual description uses a Newton–Cartan–like limit with a base $AdS_{n+2}$ and a fiber, yielding time-only correlators on the boundary and explicit bulk constructions for $N$-point functions. Field-theory correlators are obtained by contracting relativistic CFT data, yielding two-point functions $\sim t_{12}^{-\Delta}$ and $N$-point functions that depend only on time differences $t_{i2}$, fixed by Ward identities, while gravity realizes these correlators via AdS/CFT with a modified measure from the fiber. The framework provides a cohesive holographic description of non-relativistic conformal theories and suggests avenues for finite-temperature generalizations and connections to gauge theories through BMN-like limits.

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.