Galilean Yang-Mills Theory

TL;DR

This paper explores the non-relativistic limits of Yang-Mills theories, revealing new sectors with infinite Galilean Conformal symmetries, thus providing the first examples of interacting Galilean Conformal Field Theories in four dimensions.

Contribution

It systematically analyzes various Galilean limits of Yang-Mills theories, discovering infinite-dimensional symmetries and establishing the existence of interacting Galilean Conformal Field Theories in higher dimensions.

Findings

Different Galilean limits lead to distinct sectors of Yang-Mills theories.

Each sector exhibits infinite Galilean Conformal symmetries in four dimensions.

First examples of interacting Galilean Conformal Field Theories in D>2.

Abstract

We investigate the symmetry structure of the non-relativistic limit of Yang-Mills theories. Generalising previous results in the Galilean limit of electrodynamics, we discover that for Yang-Mills theories there are a variety of limits inside the Galilean regime. We first explicitly work with the $SU(2)$ theory and then generalise to $SU(N)$ for all $N$, systematising our notation and analysis. We discover that the whole family of limits lead to different sectors of Galilean Yang-Mills theories and the equations of motion in each sector exhibit hitherto undiscovered infinite dimensional symmetries, viz. infinite Galilean Conformal symmetries in $D=4$. These provide the first examples of interacting Galilean Conformal Field Theories (GCFTs) in $D>2$.