Wess-Zumino-Witten Model for Galilean Conformal Algebra

TL;DR

This paper constructs a Wess-Zumino-Witten model based on the Galilean conformal algebra, providing exact backgrounds and verifying conformal invariance in a nonrelativistic setting.

Contribution

It introduces a novel Wess-Zumino-Witten model for the Galilean conformal algebra and demonstrates its conformal invariance and potential physical relevance.

Findings

Exact six-dimensional background with central charge c=6

Verification of conformal invariance via Sugawara construction

Discussion on the physical viability of the background as spacetime

Abstract

In this note, we construct a Wess-Zumino-Witten model based on the Galilean conformal algebra in 2-spacetime dimensions, which is a nonrelativistic analogue of the relativistic conformal algebra. We obtain exact background corresponding to \sigma-models in six dimensions (the dimension of the group manifold) and a central charge c=6. We carry out a Sugawara type construction to verify the conformal invariance of the model. Further, we discuss the feasibility of the background obtained as a physical spacetime metric.