Non-semisimple Levin-Wen Models and Hermitian TQFTs from quantum (super)groups
Quantum Algebra
2024-01-22 v1 Strongly Correlated Electrons
Geometric Topology
Quantum Physics
Abstract
We develop the categorical context for defining Hermitian non-semisimple TQFTs. We prove that relative Hermitian modular categories give rise to modified Hermitian WRT-TQFTs and provide numerous examples of these structures coming from the representation theory of quantum groups and quantum superalgebras. The Hermitian theory developed here for the modified Turaev-Viro TQFT is applied to define new pseudo-Hermitian topological phases that can be considered as non-semisimple analogs of Levin-Wen models.
Keywords
Cite
@article{arxiv.2208.14566,
title = {Non-semisimple Levin-Wen Models and Hermitian TQFTs from quantum (super)groups},
author = {Nathan Geer and Aaron D. Lauda and Bertrand Patureau-Mirand and Joshua Sussan},
journal= {arXiv preprint arXiv:2208.14566},
year = {2024}
}
Comments
39 pages, tikz figures