Orbifolds and minimal modular extensions

Authors

Chongying Dong, Baskin School of Engineering
Siu Hung Ng, Louisiana State University
Li Ren, Sichuan University

Document Type

Article

Publication Date

2-1-2025

Abstract

Let V be a simple vertex operator algebra and G a finite automorphism group of V such that V^G is regular, and the conformal weight of any irreducible g-twisted V-module N for g∈G is nonnegative and is zero if and only if N=V. It is established that if V is holomorphic, then the V^G-module category CV^G is a minimal modular extension of E=Rep(G), and is equivalent to the Drinfeld center Z(VecG^α) as modular tensor categories for some α∈H³(G,S¹) with a canonical embedding of E. Moreover, the collection Mv(E) of equivalence classes of the minimal modular extensions CV^G of E for holomorphic vertex operator algebras V with a G-action forms a group, which is isomorphic to a subgroup of H³(G,S¹). Furthermore, any pointed modular category Z(VecG^α) is equivalent to CVL^G for some positive definite even unimodular lattice L. In general, for any rational vertex operator algebra U with a G-action, CU^G is a minimal modular extension of the braided fusion subcategory F generated by the U^G-submodules of U-modules. Furthermore, the group Mv(E) acts freely on the set of equivalence classes Mv(F) of the minimal modular extensions CW^G of F for any rational vertex operator algebra W with a G-action.

Publication Source (Journal or Book title)

Advances in Mathematics

Recommended Citation

Dong, C., Ng, S., & Ren, L. (2025). Orbifolds and minimal modular extensions. Advances in Mathematics, 462 https://doi.org/10.1016/j.aim.2025.110103