Pointed Drinfeld center functor

TL;DR

This paper introduces the pointed Drinfeld center functor, a new symmetric monoidal equivalence that generalizes previous concepts and models the boundary-bulk relation in 1+1D rational conformal field theories.

Contribution

It generalizes the functoriality of the full center to all fusion categories, creating a new center functor that captures boundary-bulk relations in RCFTs.

Findings

Proves the pointed Drinfeld center functor is a symmetric monoidal equivalence.

Provides a mathematical formulation of boundary-bulk relations in 1+1D RCFT.

Solves the problem of computing fusion of wall CFTs along bulk RCFTs.

Abstract

In this work, using the functoriality of Drinfeld center of fusion categories, we generalize an earlier result on the functoriality of full center of simple separable algebras in a fixed fusion category to all fusion categories. This generalization produces a new center functor, which involves both Drinfeld center and full center and will be called the pointed Drinfeld center functor. We prove that this pointed Drinfeld center functor is a symmetric monoidal equivalence. It turns out that this functor provides a precise and rather complete mathematical formulation of the boundary-bulk relation of 1+1D rational conformal field theories (RCFT). In this process, we solve an old problem of computing the fusion of two 0D (or 1D) wall CFT's along a non-trivial 1+1D bulk RCFT.