Cohomology in algebra, geometry, physicsand statistics

Boundary conditions and edge modes in gauge theories

The fields of a classical gauge theory form a smooth groupoid (aka stack) with morphisms given by gauge transformations. From this perspective, the concept of "equality" of two gauge fields A and A' is not a property but rather additional data given by the choice of a gauge transformation A ---> A' which witnesses that A and A' are "the same". In this talk, I will explain how this higher-categorical point of view is useful to study gauge theories on manifolds with boundaries and defects. In particular, I will show that the additional data witnessing boundary conditions are precisely the famous edge modes from physics. As examples, I will discuss 3d Abelian Chern-Simons theory on manifolds with boundary, which is physically describing the quantum Hall system, and also the 4d holomorphic Chern-Simons theory of Costello and Yamazaki where the edge modes on surface defects determine 2d integrable field theories.

This talk is based on arXiv:1907.10651 and arXiv:2008.01829.

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We shall meet in the blue lecture room in Zitna 25 and at ZOOM at the same time.

 The lecture room and ZOOM shall be opened at 11.15 and closed at 13.00.
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 https://cesnet.zoom.us/j/99598413922?pwd=c2Y0TENuZHdDQ3hDWEkySFI3YWo3QT09
Meeting ID: 995 9841 3922
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