Comments on Galilean conformal field theories and their geometric realization

TL;DR

This paper explores non-relativistic conformal algebras, especially the exotic conformal Galilei algebra, and their geometric realization, providing insights into their structure and potential holographic applications.

Contribution

It introduces a geometric realization of the exotic conformal Galilei algebra and analyzes non-relativistic conformal field theories with this symmetry.

Findings

Existence of an exotic central extension in 2D

Construction of a metric invariant under the exotic algebra

Discussion of holographic calculations in this background

Abstract

We discuss non-relativistic conformal algebras generalizing the Schr\"odinger algebra. One instance of these algebras is a conformal, acceleration-extended, Galilei algebra, which arises also as a contraction of the relativistic conformal algebra. In two dimensions, this admits an "exotic" central extension, whereby boosts do not commute. We study general properties of non-relativistic conformal field theories with such symmetry. We realize geometrically the symmetry in terms of a metric invariant under the exotic conformal Galilei algebra, although its signature is neither Lorentzian nor Euclidean. We comment on holographic-type calculations in this background.