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

N=2 Minimal Conformal Field Theories and Matrix Bifactorisations of x d 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications in Mathematical Physics Springer Journals

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

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Physics; Theoretical, Mathematical and Computational Physics; Mathematical Physics; Quantum Physics; Complex Systems; Classical and Quantum Gravitation, Relativity Theory
ISSN
0010-3616
eISSN
1432-0916
D.O.I.
10.1007/s00220-018-3086-z
Publisher site
See Article on Publisher Site

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 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.

Journal

Communications in Mathematical PhysicsSpringer Journals

Published: Feb 7, 2018

References

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