Higher (gauged) Wess--Zumino--Witten terms based on Lie crossed modules

2026/04/12 by Danhua Song · 1 voice
Physics and Astronomy · #math-ph

paper · pdf · doi:10.1016/j.physletb.2026.140568

arxiv published 2026/04/12 · arxiv updated 2026/05/24

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 (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.

Citations

• 5d 2-Chern-Simons theory and 3d integrable field theories
• Topological gravity and gauged Wess–Zumino–Witten term
• Lie 2-Bialgebras
• An Invitation to Higher Gauge Theory
• The Extended Cartan Homotopy Formula and a Subspace Separation Method for Chern--Simons Theory
• Transgression forms and extensions of Chern-Simons gauge theories
• Higher Gauge Theory
• Finite action principle for Chern-Simons AdS gravity
• Higher gauge theory -- differential versus integral formulation
• Global aspects of current algebra

Discussions

• Going to have to read this https://arxiv.org/abs/2604.10416 [bsky, 1 points, 0 comments]

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