Higher (gauged) Wess--Zumino--Witten terms based on Lie crossed modules
Abstract
We derive higher Wess--Zumino--Witten (WZW) and gauged WZW (gWZW) terms within strict higher Chern--Simons (CS) gauge theory. Starting from the Cartan homotopy formula, we obtain the -dimensional higher CS forms and transgression forms for strict Lie 2-groups presented by Lie crossed modules. Given two 2-connections related by a higher gauge transformation, higher transgression forms yield canonical higher WZW and gWZW terms. We prove that, for the symmetric invariant polynomial associated with differential crossed modules, the pure-gauge higher WZW term vanishes identically, whereas the higher gWZW term is exact. Consequently, the higher CS action is higher-gauge invariant on closed manifolds, and on manifolds with boundary all gauge dependence is encoded in boundary terms.
Keywords
Cite
@article{arxiv.2604.10416,
title = {Higher (gauged) Wess--Zumino--Witten terms based on Lie crossed modules},
author = {Danhua Song},
journal= {arXiv preprint arXiv:2604.10416},
year = {2026}
}