Landau-Ginzburg/Conformal field theory correspondence for xd and module tensor categories

Ros Camacho, Ana ORCID: https://orcid.org/0000-0001-9947-203X and Wasserman, Thomas A. 2024. Landau-Ginzburg/Conformal field theory correspondence for xd and module tensor categories. Journal of Mathematical Physics 65 , 121701. 10.1063/5.0184941

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Abstract

The Landau–Ginzburg/Conformal Field Theory (LG/CFT) correspondence predicts tensor equivalences between categories of matrix factorisations of certain polynomials and categories associated to the N = 2 supersymmetric conformal field theories. We realise this correspondence for the potential xd for any d ≥ 2, where previous results were limited to odd d. Our proof first establishes the fact that both sides of the correspondence carry the structure of module tensor categories over the category of -graded vector spaces equipped with a non-trivial braiding. This allows us to describe the CFT side as generated by a single object as a module tensor category, and use this to efficiently provide a functor realising the tensor equivalence.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	American Institute of Physics
ISSN:	0022-2488
Date of First Compliant Deposit:	12 November 2024
Date of Acceptance:	6 November 2024
Last Modified:	09 Jan 2025 15:15
URI:	https://orca.cardiff.ac.uk/id/eprint/173904

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