Canonical gauges in higher gauge theory

Abstract

We study the problem of finding good gauges for connections in higher gauge theories. We find that, for $2$-connections in strict $2$-gauge theory and $3$-connections in $3$-gauge theory, there are local "Coulomb gauges" that are more canonical than in classical gauge theory. In particular, they are essentially unique, and no smallness of curvature is needed in the critical dimensions. We give natural definitions of $2$-Yang-Mills and $3$-Yang-Mills theory and find that the choice of good gauges makes them essentially linear. As an application, (anti-)selfdual $2$-connections over $B^6$ are always $2$-Yang-Mills, and (anti-)selfdual $3$-connections over $B^8$ are always $3$-Yang-Mills.

References in corpus (4)

• An Invitation to Higher Gauge Theory
• Higher Yang-Mills Theory
• Six-Dimensional Superconformal Field Theories from Principal 3-Bundles over Twistor Space
• Higher Poincare Lemma and Integrability

Cited by in corpus (9)

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• 3-form Yang-Mills based on 2-crossed modules
• Higher Gauge Theory
• Explicit Non-Abelian Gerbes with Connections
• $E_2{L}_{\infty }$-algebras, Generalized Geometry, and Tensor Hierarchies
• Rota-Baxter operators on crossed modules of Lie groups and categorical solutions of the Yang-Baxter equation