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Introduction to topological quantum field theory (with defects) - Lecture 1

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BIDW01 - The Physics and Mathematics of Boundaries, Impurities, and Defects

These lectures give an introduction to the (higher) categorical approach to topological quantum field theories. We start with a brief review of symmetric monoidal categories, and define TQF Ts as symmetric monoidal functors on bordism categories. After some classification results in low dimension in the case without defects, we move on to the case with defects, i.e. when bordisms are non-trivially stratified. Here we explain general results on how to obtain n-categories from n-dimensional defect TQF Ts for n in {1,2,3}, and we describe the case of lattice models (or state sum models) in more detail. Time permitting, we also discuss the general theory of gauging not-necessarily-invertible symmetries described in terms of topological defects. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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