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arXiv · 1004.2307

Topological Field Theory, Higher Categories, and Their Applications

Anton Kapustin
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Abstract

It has been common wisdom among mathematicians that Extended Topological Field Theory in dimensions higher than two is naturally formulated in terms of n-categories with n> 1. Recently the physical meaning of these higher categorical structures has been recognized and concrete examples of Extended TFTs have been constructed. Some of these examples, like the Rozansky-Witten model, are of geometric nature, while others are related to representation theory. I outline two application of higher-dimensional TFTs. One is related to the problem of classifying monoidal deformations of the derived category of coherent sheaves, and the other one is geometric Langlands duality.

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Anton Kapustin. 2010-04-22. Topological Field Theory, Higher Categories, and Their Applications. https://arxiv.org/abs/1004.2307

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