A relative tensor product of subfactors over a modular tensor category

TL;DR

This paper introduces a new mathematical framework for combining subfactors over a modular tensor category, providing insights into fusion rules, conformal nets, and topological phase interfaces.

Contribution

It defines a relative tensor product of subfactors over a modular tensor category, linking conformal nets, fusion rules, and gapped domain wall compositions.

Findings

Provides a new realization of fusion rules of modular invariants.

Offers a mathematical definition for composing gapped domain walls.

Connects subfactor theory with topological phases and conformal nets.

Abstract

We define and study a certain relative tensor product of subfactors over a modular tensor category. This gives a relative tensor product of two completely rational heterotic full local conformal nets with trivial superselection structures over a common chiral representation category. In particular, we have a new realization of fusion rules of modular invariants. This also gives a mathematical definition of a composition of two gapped domain walls between topological phases.