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Mathematics, Quantum Algebra, High Energy Physics - Theory, Mathematics, Category Theory
Abstract:
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 representa-tions 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.
