Decorated TQFTs and their Hilbert spaces

Jagadale, Mrunmay

doi:10.1007/jhep08(2023)110

Title: Decorated TQFTs and their Hilbert spaces

Journal Article · 18 August 2023 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep08(2023)110 · OSTI ID:2420111

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California Institute of Technology (CalTech), Pasadena, CA (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)

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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Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0011632

OSTI ID:: 2420111

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 8 Vol. 2023; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Chern-Simons theories
Differential and algebraic geometry
Physics
Quantum groups
Topological field theories

Title: Decorated TQFTs and their Hilbert spaces

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