Galilean Field Theories and Conformal Structure

TL;DR

This paper explores non-relativistic Galilean field theories, revealing that they exhibit an infinite-dimensional conformal symmetry, which is a significant enhancement over relativistic conformal invariance, across various models and dimensions.

Contribution

It demonstrates that Galilean field theories derived from relativistic conformal theories possess an infinite-dimensional Galilean conformal symmetry, a novel and unexpected feature.

Findings

Galilean conformal structure is infinite dimensional in all studied cases.

Non-relativistic limits lead to multiple sectors with enhanced symmetries.

Infinite symmetry enhancement is a generic feature of conformal theories in any dimension.

Abstract

We perform a detailed analysis of Galilean field theories, starting with free theories and then interacting theories. We consider non-relativistic versions of massless scalar and Dirac field theories before we go on to review our previous construction of Galilean Electrodynamics and Galilean Yang-Mills theory. We show that in all these cases, the field theories exhibit non-relativistic conformal structure (in appropriate dimensions). The surprising aspect of the analysis is that the non-relativistic conformal structure exhibited by these theories, unlike relativistic conformal invariance, becomes infinite dimensional even in spacetime dimensions greater than two. We then couple matter with Galilean gauge theories and show that there is a myriad of different sectors that arise in the non-relativistic limit from the parent relativistic theories. In every case, if the parent relativistic theory exhibited conformal invariance, we find an infinitely enhanced Galilean conformal invariance in the non-relativistic case. This leads us to suggest that infinite enhancement of symmetries in the non-relativistic limit is a generic feature of conformal field theories in any dimension.