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Decorated TQFTs and their Hilbert Spaces (2206.14967v1)
Published 30 Jun 2022 in hep-th, math-ph, math.GT, and math.MP
Abstract: We discuss topological quantum field theories that compute topological invariants which depend on additional structures (or decorations) on three-manifolds. The $q$-series invariant $\hat{Z}(q)$ proposed by Gukov, Pei, Putrov and Vafa is an example of such an invariant. We describe how to obtain these decorated invariants by cutting and gluing, and make a proposal for Hilbert spaces that are assigned to two-dimensional surfaces in the $\hat{Z}$-TQFT.
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