Higher central charges and Witt groups
Quantum Algebra
2022-04-12 v3 Category Theory
Number Theory
Abstract
In this paper, we introduce the definitions of signatures of braided fusion categories, which are proved to be invariants of their Witt equivalence classes. These signature assignments define group homomorphisms on the Witt group. The higher central charges of pseudounitary modular categories can be expressed in terms of these signatures, which are applied to prove that the Ising modular categories have infinitely many square roots in the Witt group. This result is further applied to prove a conjecture of Davydov-Nikshych-Ostrik on the super-Witt group: the torsion subgroup generated by the completely anisotropic s-simple braided fusion categories has infinite rank.
Cite
@article{arxiv.2002.03570,
title = {Higher central charges and Witt groups},
author = {Siu-Hung Ng and Eric C. Rowell and Yilong Wang and Qing Zhang},
journal= {arXiv preprint arXiv:2002.03570},
year = {2022}
}
Comments
34 pages. Some typos and an extra reference are removed