Communications in Mathematical Physics

, Volume 357, Issue 2, pp 597–629 | Cite as

N=2 Minimal Conformal Field Theories and Matrix Bifactorisations of x d

  • Alexei Davydov
  • Ana Ros Camacho
  • Ingo RunkelEmail author


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.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsOhio UniversityAthensUSA
  2. 2.Mathematisch InstituutUniversiteit UtrechtUtrechtThe Netherlands
  3. 3.Fachbereich MathematikUniversität HamburgHamburgGermany

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