Higher-group structure in $2n$-dimensional axion-electrodynamics

TL;DR

This paper explores the higher-group structure in 2n-dimensional axion electrodynamics, focusing on the n=3 case, revealing complex algebraic relations and anomalies that deepen understanding of symmetries in higher-dimensional gauge theories.

Contribution

It uncovers a higher-group structure in 2n-dimensional axion-electrodynamics, especially for n=3, highlighting a multi-ary operation among symmetry generators and associated anomalies.

Findings

Identified higher-group structure in 2n-dimensional axion electrodynamics.

Derived correlation function identities using gauge transformations.

Discovered multi-ary operations in the symmetry algebra for n=3.

Abstract

We investigate $2n$-dimensional axion electrodynamics for the purpose of exploring a higher-group structure underlying it. This is manifested as a Green-Schwarz transformation of the background gauge fields that couple minimally to the conserved currents. The $n=3$ case is studied most intensively. We derive the identities of correlation functions among the global symmetry generators by using a gauge transformation that maps two correlation functions with each other. A key ingredient in this computation is given by the Green-Schwarz transformation and the 't Hooft anomalies associated with the gauge transformation. The algebraic structure of these results and its physical interpretations are discussed in detail. In particular, we find that the higher-group structure for $n=3$ is endowed with a multi-ary operation among the symmetry generators.