N =2 Minimal Conformal Field Theories and Matrix Bifactorisations of xd.

We establish an action of the representations of N = 2-superconformal symmetry on the category of matrix factorisations of the potentials x^d and x^d - y^d, for d odd. More precisely we prove a tensor equivalence between (a) the category of Neveu-Schwarz-type representations of the N = 2 minimal super vertex operator algebra at central charge 3-6/d, and (b) a full subcategory of graded matrix factorisations of the potential x^d - y^d. The subcategory in (b) is given by permutation-type matrix factorisations with consecutive index sets. 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 [BR], where an isomorphism of fusion rules was established. [ABSTRACT FROM AUTHOR]