Modular tensor categories, subcategories, and Galois orbits

TL;DR

This paper investigates the interaction between Galois actions and fusion subcategories in modular tensor categories, providing classifications and characterizations relevant to their structure and symmetries.

Contribution

It introduces new results on Galois actions on modular tensor categories, including classifications of subcategories and categories with specific Galois orbit structures.

Findings

Characterization of Galois-closed fusion subcategories

Classification of categories factoring as pointed and transitive

Identification of categories with two Galois orbits and nontrivial grading

Abstract

We establish a set of general results to study how the Galois action on modular tensor categories interacts with fusion subcategories. This includes a characterization of fusion subcategories of modular tensor categories which are closed under the Galois action, and a classifcation of modular tensor categories which factor as a product of pointed and transitive categories in terms of pseudoinvertible objects. As an application, we classify modular tensor categories with two Galois orbits of simple objects and a nontrivial grading group.