Higher Structure Conferences Waldorf (Rev #1, changes)

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Transgression of n-bundles and extended field theories

Abstract: I will try to explain how an n-bundle with connection can be regarded as the value of an n-dimensional topological field theory on the point. The values on higher dimensional manifolds are then derived by transgression, with the holonomy functional of the n-bundle in top dimension. I will discuss situations in which the converse question, i.e. whether or not a non-extended field theory can be extended all the way down to the point, has a precise answer. I will try to elucidate this in the examples of B-fields for sigma models and of the Chern-Simons 2-gerbe.