Supersymmetric Semisimple Cardy-Frobenius Algebras

TL;DR

This paper classifies semisimple super Cardy-Frobenius algebras as direct sums of three simple types and explores their applications in singularity theory, Landau-Ginzburg models, and matrix factorizations.

Contribution

It provides a complete classification of semisimple super Cardy-Frobenius algebras and connects these structures to singularity theory and Landau-Ginzburg models.

Findings

Semisimple super Cardy-Frobenius algebras decompose into three simple types.

The classification aids in understanding algebraic structures in topological field theory.

Applications to singularity theory and matrix factorizations are demonstrated.

Abstract

Cardy-Frobenius algebra is the algebraic structure on the space of states in open-closed topological field theory. We prove that every semisimple super Cardy-Frobenius algebras is the direct sum of the super Cardy-Frobenius algebras of three simple types. We also apply our results to singularity theory via Landau-Ginzburg models and matrix factorizations.