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 $(2n+2)$-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.

References in corpus (5)

• The Extended Cartan Homotopy Formula and a Subspace Separation Method for Chern--Simons Theory
• 4-d semistrict higher Chern-Simons theory I
• Higher Chern-Simons-Antoniadis-Savvidy forms based on crossed modules
• Higher Chern-Simons based on (2-)crossed modules
• Extended Cartan homotopy formula for higher Chern-Simons-Antoniadis-Savvidy theory