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.
Cite
@article{arxiv.1208.1481,
title = {Adjunctions and defects in Landau-Ginzburg models},
author = {Nils Carqueville and Daniel Murfet},
journal= {arXiv preprint arXiv:1208.1481},
year = {2015}
}
Comments
58 pages; v2: Fixed typos and references, removed comments about graded matrix factorisations; v3: exposition improved and shortened, main result now holds over an arbitrary ring k; v4: many improvements to exposition