N=2 minimal conformal field theories and matrix bifactorisations of xd

Davydov, Alexei; Camacho, Ana Ros; Runkel, Ingo

doi:10.1007/s00220-018-3086-z

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

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Davydov, Alexei
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s00220-018-3086-z
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Davydov, A., Camacho, A. R., & Runkel, I. (2018). N=2 minimal conformal field theories and matrix bifactorisations of x^d. Communications in Mathematical Physics, 357(2), 597-629. doi:10.1007/s00220-018-3086-z.

Cite as: https://hdl.handle.net/21.11116/0000-0004-4777-7

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.