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Citation: Geer, Nathan, et al. "Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTs." Annals of Physics 442 (2022): 168937.
Tags: xy-anyons, Mathematical
There has recently been a growing literature on non-semisimple MTCs/TQFTs. This paper observes that non-semisimple MTCs often naturally have pseudo-Hermitian structures, which allows them to be integrated into the Levin-Wen model to give non-semisimple TQFTs.
One of the big algebraic tools used in this paper is the idea of "unrolled" quantum groups. The representations of unrolled quantum groups naturally give non-semisimple TQFTs, and hence serve as the canonical examples of this new class of objects.