Gauging in Parameter Space: A Top-Down Perspective

TL;DR

This paper introduces a top-down approach to gauging parameters in quantum field theories by promoting them to dynamical fields, revealing new symmetry structures and topological defects across dimensions.

Contribution

It presents a systematic framework for gauging parameters as dynamical fields, connecting to generalized symmetries and topological defects, with applications to super Yang-Mills and ABJ(M) theories.

Findings

New topological defects identified in gauged parameter spaces.

Systematic derivation of symmetry theories for parameters.

Applications to 4D super Yang-Mills and 3D ABJ(M) theories.

Abstract

In this paper, we discuss a novel top-down perspective on gauging parameters in quantum field theories (QFTs) by promoting them to partially dynamical fields. Through a generalized notion of symmetry theories, we explore the consequences of this promotion, revealing new topological defects, decompositions as well as generalized symmetry structures across various dimensions. We provide a systematic top-down derivation of symmetry theories for parameters and discuss how special types of branes, such as Euclidean branes and fluxbranes are related to gauging in the parameter space in QFTs. We illustrate our theoretical framework with two key examples: the modified instanton sum in 4D $\mathcal{N}=4$ super Yang-Mills theory and the gauging of gauge ranks in 3D ABJ(M) theories.