A test for emergent dynamics

TL;DR

This paper introduces a generalized maximization method that helps identify emergent symmetries in quantum field theories by detecting maximum R-charges, offering a new tool for analyzing gauge symmetries.

Contribution

It proposes a novel generalization of a-maximization that maximizes a function under inequalities, enabling the detection of emergent symmetries in theoretical models.

Findings

Maximum R-charge indicates absence of emergent symmetries

Method detects emergent Abelian and non-Abelian gauge symmetries

Provides a new criterion for symmetry emergence in quantum field theories

Abstract

A generalization of a-maximization is proposed that maximizes a subject to inequalities rather than equalities. The implication of this conjecture is that in the absence of emergent symmetries, there is a maximum R-charge for fields appearing in the path integral. This maximum R-charge leads to a novel way of detecting emergent Abelian symmetries and non-Abelian gauge symmetries.