Landau–Ginzburg/conformal field theory correspondence for x d and module tensor categories
Year: 2024
Type: article
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 Zd-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.
Source: Journal of Mathematical Physics
DOI: 10.1063/5.0184941
Authors: Ana Ros Camacho, Thomas A. Wasserman
Institutions: Cardiff University, University of Oxford
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Funder: Cardiff University
OpenAlex ID: W4404963529