Emergent gauge symmetries: Yang-Mills theory

TL;DR

This paper establishes general conditions under which gauge symmetries emerge in interacting vector field theories, demonstrating that these conditions lead to Yang-Mills theories at low energies.

Contribution

It extends previous mechanisms for emergent gauge symmetries to non-Abelian cases, providing a set of criteria that ensure the emergence of Yang-Mills theories.

Findings

Conditions guarantee the removal of unphysical states.

Emergence of gauge symmetries is proven to be equivalent to these conditions.

Theories satisfying these conditions are shown to be low-energy Yang-Mills theories.

Abstract

Gauge symmetries remove unphysical states and guarantee that field theories are free from the pathologies associated with these states. In this work we find a set of general conditions that guarantee the removal of unphysical states in field theories describing interacting vector fields. These conditions are obtained through the extension of a mechanism for the emergence of gauge symmetries proposed in a previous article [C. Barcel\'o et al. JHEP 10 (2016) 084] in order to account for non-Abelian gauge symmetries, and are the following: low-energy Lorentz invariance, emergence of massless vector fields describable by an action quadratic in those fields and their derivatives, and self-coupling to a conserved current associated with specific rigid symmetries. Using a bootstrapping procedure, we prove that these conditions are equivalent to the emergence of gauge symmetries and, therefore, guarantee that any theory satisfying them must be equivalent to a Yang-Mills theory at low energies.