home | literature reviews

"Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTs", Nathan Geer, et al., 2022

Reviewed September 4, 2023

Citation: Geer, Nathan, et al. "Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTs." Annals of Physics 442 (2022): 168937.

Web: https://arxiv.org/abs/2108.10798

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.