Fusion of interfaces in Landau-Ginzburg models: a functorial approach

TL;DR

This paper introduces a functorial method to compute the fusion of B-type interfaces in Landau-Ginzburg models, simplifying calculations and enabling the construction of all rational B-type defects in certain models.

Contribution

It proposes a novel functorial framework for interface fusion in Landau-Ginzburg models, extending the category of matrix factorizations to streamline computations.

Findings

Fusion functors effectively compute interface fusion.

The approach applies to minimal and Kazama-Suzuki models.

All rational B-type defects can be generated from elementary defects.

Abstract

We investigate the fusion of B-type interfaces in two-dimensional supersymmetric Landau-Ginzburg models. In particular, we propose to describe the fusion of an interface in terms of a fusion functor that acts on the category of modules of the underlying polynomial rings of chiral superfields. This uplift of a functor on the category of matrix factorisations simplifies the actual computation of interface fusion. Besides a brief discussion of minimal models, we illustrate the power of this approach in the SU(3)/U(2) Kazama-Suzuki model where we find fusion functors for a set of elementary topological defects from which all rational B-type topological defects can be generated.