Three-Dimensional Spin TFTs from Gauging Line Defects
arxiv(2024)
Abstract
From the input of an oriented three-dimensional TFT with framed line defects
and a commutative Δ-separable Frobenius algebra A in the ribbon
category of these line defects, we construct a three-dimensional spin TFT. The
framed line defects of the spin TFT are labelled by certain equivariant modules
over A, and the spin structure may or may not extend to a given line defect.
Physically the spin TFT can be interpreted as the result of gauging a one-form
symmetry in the original oriented TFT. This spin TFT extends earlier
constructions in Blanchet-Masbaum (1996) and Blanchet (2005)
[arXiv:math/0303240], and it reproduces the classification of abelian spin
Chern-Simons theories in Belov-Moore (2005) [arXiv:hep-th/0505235].
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