Carrollian Yang-Mills Theory

TL;DR

This paper develops a Carrollian limit of Yang-Mills theory, constructing multiple sectors with distinct interactions, analyzing their symmetries, and computing propagators and vertices, revealing ultra-local behavior.

Contribution

It introduces four sectors of Carrollian Yang-Mills theory with different interaction structures and analyzes their symmetries and propagators, expanding the understanding of ultra-local gauge theories.

Findings

All sectors are invariant under infinite Carrollian Conformal symmetry.

No central extensions in charge algebra at phase space level.

Propagators exhibit ultra-local behavior in position space.

Abstract

By doing a small $c$ (speed of light) expansion of $SU(N)$ Yang-Mills fields, we construct two different electric and two different magnetic sectors actions of Carrollian Yang-Mills theory. For both electric and magnetic cases, one sector contains non-trivial self-interaction, and another is $N^2-1$ copies of respective sector Carrollian abelian theory. In $d=4$ , all the four sectors are invariant under infinite Carrollian Conformal symmetry. There are no central extensions when analyzing charge algebra at the phase space level. Lastly, we compute propagators for all four sectors and vertices for two non-trivial sectors. Propagators in position space show ultra-local behavior.