On Representations and Correlation Functions of Galilean Conformal Algebras

TL;DR

This paper analyzes the Galilean Conformal Algebra (GCA) obtained via a non-relativistic contraction of the relativistic conformal group, focusing on its surprisingly natural infinite-dimensional extension and detailing the representations. It then derives explicit two- and three-point non-relativistic conformal correlation functions for GCA quasi-primaries, highlighting how the GCA’s extended symmetries constrain correlators more tightly than the Schrödinger algebra yet differently from relativistic CFTs. The work contrasts GCA correlators with those of relativistic CFTs and Schrödinger symmetry, clarifying the role of rapidity and the absence of a mass central term. Finally, it outlines a bulk dual picture akin to an AdS2/CFT1 framework via a Newton-Cartan-like geometry and discusses future directions, including potential bulk-boundary mappings.Overall, the paper advances the structural understanding of non-relativistic conformal symmetries and their physical implications for correlation functions and holography.

Abstract

Galilean Conformal Algebras (GCA) have been recently proposed as a different non-relativistic limit of the AdS/CFT conjecture. In this note, we look at the representations of the GCA. We also construct explicitly the two and three point correlators in this non-relativistic limit of CFT and comment on the differences with the relativistic case and also the more studied Schrodinger group.