Nonabelian Surface Holonomy from Multiplicative Integration (online meeting)

Surface holonomy and the Wess–Zumino phase are fundamental in string theory and Chern–Simons theory, but giving a fully analytic description of their nonabelian versions has been a longstanding challenge. In this talk, I will explain how Yekutieli’s theory of nonabelian multiplicative integration on surfaces provides such a framework. The starting point is a smooth 2-connection (α,β) on a Lie crossed module. I will describe how one constructs multiplicative integrals associated to this data, and then show that these integrals satisfy the axioms of a transport 2-functor in the sense of Schreiber and Waldorf, providing an explicit model of nonabelian surface holonomy. I will conclude by discussing the resulting three-dimensional Stokes theorem and its relation to the Wess–Zumino phase, including the abelian case as a special instance.