The classifying algebra for defects

TL;DR

This paper introduces a classifying algebra framework for topological defects in rational conformal field theories, linking algebraic structures to defect transmission and partition functions.

Contribution

It establishes that topological defects can be characterized by a finite-dimensional algebra whose representations encode defect transmission coefficients.

Findings

Classifying algebra structure constants are traces of operators on conformal blocks

Defect transmission coefficients determine defect partition functions

The algebraic approach unifies defect classification in rational CFTs

Abstract

We demonstrate that topological defects in a rational conformal field theory can be described by a classifying algebra for defects - a finite-dimensional semisimple unital commutative associative algebra whose irreducible representations give the defect transmission coefficients. We show in particular that the structure constants of the classifying algebra are traces of operators on spaces of conformal blocks and that the defect transmission coefficients determine the defect partition functions.