Landau–Ginzburg/conformal field theory correspondence for <i>x</i> <i>d</i> and module tensor categories

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.