Title
Higher central charges and Witt groups
Document Type
Article
Publication Date
2022
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 modulo the pointed part. 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.
Publication Source (Journal or Book title)
Advances in Mathematics
Recommended Citation
Ng, S., Rowell, E., Wang, Y., & Zhang, Q. (2022). Higher central charges and Witt groups. Advances in Mathematics, 404 https://doi.org/10.1016/j.aim.2022.108388