On fusing matrices associated with conformal boundary conditions

TL;DR

This paper studies the structure and computation of fusing matrices related to open topological defects in rational conformal field theories, using topological field theory methods and Frobenius algebra objects.

Contribution

It introduces a general framework for understanding and calculating fusing matrices for open defects in RCFTs via Frobenius algebra objects in modular tensor categories.

Findings

Derived explicit formulas for fusing matrices in rational free boson theories

Provided a topological field theory approach to compute defect-related matrices

Discussed applications to boundary renormalisation group flows

Abstract

In the context of rational conformal field theories (RCFT) we look at the fusing matrices that arise when a topological defect is attached to a conformal boundary condition. We call such junctions open topological defects. One type of fusing matrices arises when two open defects fuse while another arises when an open defect passes through a boundary operator. We use the topological field theory approach to RCFTs based on Frobenius algebra objects in modular tensor categories to describe the general structure associated with such matrices and how to compute them from a given Frobenius algebra object and its representation theory. We illustrate the computational process on the rational free boson theories. Applications to boundary renormalisation group flows are briefly discussed.