Alterfold Topological Quantum Field Theory
Abstract
We introduce the 3-alterfold topological quantum field theory (TQFT) by extending the quantum invariant of 3-alterfolds. The bases of the TQFT are explicitly characterized and the Levin-Wen model is naturally interpreted in 3-alterfold TQFT bases. By naturally considering the RT TQFT and TV TQFT as sub-TQFTs within the 3-alterfold TQFT, we establish their equivalence. The 3-alterfold TQFT is unitary when the input fusion category is unitary. Additionally, we extend the 3-alterfold TQFT to the Morita context and demonstrate that Morita equivalent fusion categories yield equivalent TV TQFTs. We also provide a simple pictorial proof of complete positivity criteria for unitary categorization when the 3-alterfold TQFT is unitary. Expanding our scope to high-genus surfaces by replacing the torus, we introduce the high genus topological indicators and proving the equivariance under the mapping class group actions.
Cite
@article{arxiv.2312.06477,
title = {Alterfold Topological Quantum Field Theory},
author = {Zhengwei Liu and Shuang Ming and Yilong Wang and Jinsong Wu},
journal= {arXiv preprint arXiv:2312.06477},
year = {2023}
}
Comments
35 pages