Galilean Gauge Theories from Null Reductions

TL;DR

This paper explores how null reduction constructs Galilean gauge theories, revealing their symmetries, dualities, and quantum aspects in various spacetime dimensions, with implications for non-relativistic physics.

Contribution

It demonstrates the derivation of Galilean gauge theories via null reduction and analyzes their symmetries, dualities, and quantum features in different dimensions.

Findings

Galilean gauge theories exhibit enhanced infinite-dimensional symmetries.

Distinct non-relativistic conformal symmetries appear in 3D and 4D cases.

Non-relativistic electromagnetic duality differs between 3D and 4D theories.

Abstract

The procedure of null reduction provides a concrete way of constructing field theories with Galilean invariance. We use this to examine Galilean gauge theories, viz. Galilean electrodynamics and Yang-Mills theories in spacetime dimensions 3 and 4. Different non-relativistic conformal symmetries arise in these contexts: Schr{\"o}dinger symmetry in $d=3$ and Galilean conformal symmetry in $d=4$. A canonical analysis further reveals that the symmetries enhance to their infinite dimensional versions in phase space and pick up central extensions. In addition, for the Abelian theory, we discuss non-relativistic electro-magnetic duality in $d=3$ and its difference with the $d=4$ version. We also mention some quantum aspects for both Abelian and non-Abelian theories.