Adjunctions and defects in Landau-Ginzburg models

Abstract

We study the bicategory of Landau-Ginzburg models, which has potentials as objects and matrix factorisations as 1-morphisms. Our main result is the existence of adjoints in this bicategory and a description of evaluation and coevaluation maps in terms of Atiyah classes and homological perturbation. The bicategorical perspective offers a unified approach to Landau-Ginzburg models: we show how to compute arbitrary correlators and recover the full structure of open/closed TFT, including the Kapustin-Li disk correlator and a simple proof of the Cardy condition, in terms of defect operators which in turn are directly computable from the adjunctions.