Algorithmic deformation of matrix factorisations

TL;DR

This paper explores methods for deforming matrix factorisations in topological Landau-Ginzburg models, introducing algorithms, new generation techniques, and criteria for boundary obstructions, with practical implementations and examples.

Contribution

It presents novel algorithms for deforming matrix factorisations, including a new method using nilpotent substitutions and criteria for lifting boundary obstructions.

Findings

Implemented deformation algorithms with practical examples

Introduced a new way to generate matrix factorisations via nilpotent substitutions

Established criteria for lifting boundary obstructions

Abstract

Branes and defects in topological Landau-Ginzburg models are described by matrix factorisations. We revisit the problem of deforming them and discuss various deformation methods as well as their relations. We have implemented these algorithms and apply them to several examples. Apart from explicit results in concrete cases, this leads to a novel way to generate new matrix factorisations via nilpotent substitutions, and to criteria whether boundary obstructions can be lifted by bulk deformations.