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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.10416 |
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| _version_ | 1866913159023951872 |
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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 |