PEARSON, JAMIE,JONATHAN (2024) Gauging Generalised Symmetries : Group-Theoretic Higher Fusion Categories and Higher Representation Theory. Doctoral thesis, Durham University.
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Abstract
In this thesis we will construct novel non-invertible symmetries by
gauging finite invertible symmetries, discuss the various formalisms for performing
this construction using one and two dimensions as motivating examples, and invest-
igate what the most general notion of gauging is in three dimensions. While unitary
fusion categorical symmetries are now well under control for describing symmetries
of oriented unitary quantum field theories in two dimensions, the same cannot be
said for unitary fusion 2-categorical symmetries in three dimensions. It is our hope
that by conjecturing that all such underlying fusion 2-categories are group-theoretic,
that we can systematically construct all examples and describe how they should lift
to unitary fusion 2-categories.
| Item Type: | Thesis (Doctoral) |
|---|---|
| Award: | Doctor of Philosophy |
| Keywords: | Mathematical Physics,Quantum Field Theory, Categorical Symmetry, Category Theory, Higher Category Theory, Higher Representation Theory, Gauging, Topological Order, Gapped Phases |
| Faculty and Department: | Faculty of Science > Mathematical Sciences, Department of |
| Thesis Date: | 2024 |
| Copyright: | Copyright of this thesis is held by the author |
| Deposited On: | 07 Nov 2024 11:17 |
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