(Non)-Invertible Topology in Quantum Field Theory
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Date
2023-06-05
Authors
Yu, Matthew
Journal Title
Journal ISSN
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Publisher
University of Waterloo
Abstract
This thesis aims to highlight aspects of mathematics and physics that arise in topological
field theories. We will consider invertible and noninvertible topological theories. In the
former case, we compute the classification of these invertible theories which arise as the
trivial bulk of some anomalous theory one dimension lower. The computation tools used
here were conceived in algebraic topology and this work aims to develop these techniques for
applications to physical theories. In the latter case, to study such theories in low dimensions
we develop part of the theory of fusion 2-categories. Using techniques here allow us to
classify noninvertible phases up to equivalence.