The Symmetry Enriched Center Functor is Fully Faithful

TL;DR

This paper introduces a new mathematical framework for symmetry enriched topological orders, defining a symmetry enriched center functor that is fully faithful and captures boundary-bulk relations.

Contribution

It constructs a symmetry enriched center functor that is fully faithful, providing a rigorous mathematical description of boundary-bulk relations in SET orders.

Findings

The symmetry enriched center functor is fully faithful.

A new tensor product called the relative tensor product is introduced.

Provides a condensable algebra-based description of the tensor product.

Abstract

In this work, inspired by some physical intuitions, we define a series of symmetry enriched categories to describe symmetry enriched topological (SET) orders, and define a new tensor product, called the relative tensor product, which describes the stacking of 2+1D SET orders. Then we choose and modify the domain and codomain categories, and manage to make the Drinfeld center a fully faithful symmetric monoidal functor. It turns out that this functor, named the symmetry enriched center functor, provides a precise and rather complete mathematical formulation of the boundary-bulk relation of symmetry enriched topological (SET) orders. We also provide another description of the relative tensor product via a condensable algebra.