N=2 minimal conformal field theories and matrix bifactorisations of x^d

TL;DR

This paper establishes a tensor equivalence between certain categories of matrix factorisations and representations of N=2 minimal super vertex operator algebras, illuminating aspects of the Landau-Ginzburg / conformal field theory correspondence.

Contribution

It proves a tensor equivalence between subcategories of graded matrix factorisations and super vertex operator algebra representations, extending previous fusion rule results.

Findings

Tensor equivalence between matrix factorisations and VOA representations.

Identification of permutation-type matrix factorisations with Neveu-Schwarz representations.

Supports the Landau-Ginzburg / conformal field theory correspondence.

Abstract

We prove a tensor equivalence between full subcategories of a) graded matrix factorisations of the potential x^d-y^d and b) representations of the N=2 minimal super vertex operator algebra at central charge 3-6/d, where d is odd. The subcategories are given by a) permutation-type matrix factorisations with consecutive index sets, and b) Neveu-Schwarz-type representations. The physical motivation for this result is the Landau-Ginzburg / conformal field theory correspondence, where it amounts to the equivalence of a subset of defects on both sides of the correspondence. Our work builds on results by Brunner and Roggenkamp [arXiv:0707.0922], where an isomorphism of fusion rules was established.