Abstract
We establish an action of the representations of N = 2-superconformal symmetry on the category of matrix factorisations of the potentials xd and xd−yd, 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 xd−yd. 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.
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Davydov, A., Camacho, A.R. & Runkel, I. N=2 Minimal Conformal Field Theories and Matrix Bifactorisations of xd. Commun. Math. Phys. 357, 597–629 (2018). https://doi.org/10.1007/s00220-018-3086-z
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DOI: https://doi.org/10.1007/s00220-018-3086-z