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Main Author: Song, Danhua
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2604.10416
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author Song, Danhua
author_facet Song, Danhua
contents 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 $(2n+2)$-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.
format Preprint
id arxiv_https___arxiv_org_abs_2604_10416
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Higher (gauged) Wess--Zumino--Witten terms based on Lie crossed modules
Song, Danhua
Mathematical Physics
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 $(2n+2)$-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.
title Higher (gauged) Wess--Zumino--Witten terms based on Lie crossed modules
topic Mathematical Physics
url https://arxiv.org/abs/2604.10416