The cut operation on matrix factorisations

Abstract

The bicategory $\mathcal{LG}$ of Landau-Ginzburg models has polynomials as objects and matrix factorisations as $1$-morphisms. The composition of these $1$-morphisms produces infinite rank matrix factorisations, which is a nuisance. In this paper we define a bicategory which is equivalent to $\mathcal{LG}$ in which composition of $1$-morphisms produces finite rank matrix factorisations equipped with the action of a Clifford algebra. This amounts to a finite model of composition in $\mathcal{LG}$.