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...

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Bibliographic Details
Published in:Communications in mathematical physics 2018, Vol.357 (2), p.597-629
Main Authors: Davydov, Alexei, Camacho, Ana Ros, Runkel, Ingo
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary: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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-018-3086-z