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

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.

Automated summary

We investigate the higher-group structure underlying 2n-dimensional axion electrodynamics, which is manifested as a Green-Schwarz transformation. The n = 3 case is studied most intensively, and correlation function identities among the global symmetry generators are derived using a gauge transformation. The Green-Schwarz transformation and 't Hooft anomalies associated with the gauge transformation play a key role in this computation. The algebraic structure of the results and their physical interpretations, including a multi-ary operation among the symmetry generators for n = 3, are discussed in detail.