Matrix factorizations and the Landau-Ginzburg/conformal field theory correspondence

TL;DR

This thesis explores the mathematical aspects of the Landau-Ginzburg/conformal field theory correspondence, aiming to formalize the relation between defects in these models, which has been historically supported by examples but lacks a general proof.

Contribution

It advances the mathematical understanding of the Landau-Ginzburg/conformal field theory correspondence by proposing a formal framework for the defect relations.

Findings

Supports the conjectured relation between defects in Landau-Ginzburg and conformal field theories

Provides new mathematical insights into the Landau-Ginzburg/conformal field theory correspondence

Contributes to the ongoing effort to formalize the conjecture

Abstract

This is the author's PhD thesis, which focuses on the so-called Landau-Ginzburg/conformal field theory correspondence. This correspondence dates from the late 80s and early 90s in the physics literature and in particular, it predicts a relation between defects in Landau-Ginzburg models and defects in conformal field theories. This relation is supported by examples, but not understood in general, nor up to date is there a clear mathematical conjecture of the Landau-Ginzburg/conformal field theory correspondence. The pursuit of a precise mathematical statement of this conjecture continues to generate a rich mathematical output, and this PhD thesis is another contribution towards this end.