N=2 minimal conformal field theories and matrix bifactorisations of x^d
  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. 
Alexei Davydov, Ana Ros Camacho, Ingo Runkel
math.QA hep-th math.CT