Matrix Factorizations, Minimal Models and Massey Products

TL;DR

This paper introduces a method to compute non-linear deformations of matrix factorizations in ADE minimal models using Massey products, linking algebraic obstructions to superpotential critical loci.

Contribution

It develops an algorithm for calculating deformations via Massey products, connecting cohomological higher products to effective superpotentials in minimal models.

Findings

Algorithm computes polynomial rings encoding deformation obstructions.

Effective superpotentials match results from A-infinity relations.

Illustrated with examples, notably the E6 minimal model.

Abstract

We present a method to compute the full non-linear deformations of matrix factorizations for ADE minimal models. This method is based on the calculation of higher products in the cohomology, called Massey products. The algorithm yields a polynomial ring whose vanishing relations encode the obstructions of the deformations of the D-branes characterized by these matrix factorizations. This coincides with the critical locus of the effective superpotential which can be computed by integrating these relations. Our results for the effective superpotential are in agreement with those obtained from solving the A-infinity relations. We point out a relation to the superpotentials of Kazama-Suzuki models. We will illustrate our findings by various examples, putting emphasis on the E_6 minimal model.