The Hermitian axiom on two-dimensional topological quantum field theories

Author(s)
Zhu, Honglin
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Abstract
We examine Atiyah’s Hermitian axiom for two-dimensional complex topological quantum field theories. Building on the correspondence between 2D topological quantum field theories (TQFTs) and Frobenius algebras, we find the algebraic objects corresponding to Hermitian and unitary TQFTs, respectively, and prove structure theorems about them. We then clarify a few older results on unitary TQFTs using our structure theorems.
Date issued
2023-02-01
URI
https://hdl.handle.net/1721.1/153229
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Journal of Mathematical Physics
Publisher
AIP Publishing
Citation
Honglin Zhu; The Hermitian axiom on two-dimensional topological quantum field theories. J. Math. Phys. 1 February 2023; 64 (2): 022301.
Version: Final published version
ISSN
0022-2488
1089-7658
Keywords
Mathematical Physics, Statistical and Nonlinear Physics
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