Citation: Gustafson, Paul, Eric C. Rowell, and Yuze Ruan. "Metaplectic categories, gauging and property $ F$." Tohoku Mathematical Journal 72.3 (2020): 411-424.
Web: https://arxiv.org/abs/1808.00698
Tags: Property-F, SPT/SETs
This paper proves the property F conjecture for a large class of MTCs. Namely, M-Metaplectic categories for odd N.
What is interesting about this paper is that it highlights one property which makes weakly integral fusion categories special: it is a Galois invariant property, and hence modularity is respected to some extent by Galois action. One of the key difficulties in proving property F comes in answering the question "what makes weak integrality so special, anyways?" so this might approximate an answer.