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

Davydov, Alexei, Ros Camacho, Ana ORCID: https://orcid.org/0000-0001-9947-203X and Runkel, Ingo 2018. N=2 minimal conformal field theories and matrix bifactorisations of xd. Communications in Mathematical Physics 357 , pp. 597-629. 10.1007/s00220-018-3086-z

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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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Springer Verlag
ISSN:	0010-3616
Date of First Compliant Deposit:	14 February 2020
Date of Acceptance:	15 November 2017
Last Modified:	07 Nov 2023 06:34
URI:	https://orca.cardiff.ac.uk/id/eprint/129662

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