Galilean Yang-Mills Theory

TL;DR

The work constructs the non-relativistic (Galilean) limit of Yang–Mills theories, uncovering a rich landscape of sectors governed by a Galilean Conformal Algebra (GCA) that, in $D=4$, extends to an infinite-dimensional symmetry. Starting from the relativistic conformal invariance of YM in $D=4$, the authors systematically obtain electric, magnetic, and several skewed sectors for $SU(2)$ and then generalize to $SU(N)$, detailing scaling rules, equations of motion, and gauge invariances for each sector. Remarkably, every sector in $D=4$ supports the finite Galilean conformal invariance and, moreover, admits the full infinite GCA at the level of classical equations of motion, demonstrating a concrete interacting Galilean Conformal Field Theory (GCFT) in dimensions $>2$. The results offer a robust framework to explore non-relativistic conformal symmetries in gauge theories, with potential implications for quantum anomalies, dualities, and flat-space holography across both bosonic and supersymmetric extensions.

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 $D>2$.