Matrix factorisations and open topological string theory

TL;DR

This paper develops a method to compute all amplitudes and the effective superpotential in open topological string theory using A-infinity-categories, with applications to N=2 Landau-Ginzburg models.

Contribution

It introduces a general construction of cyclic minimal models for A-infinity-algebras and applies it to solve tree-level amplitudes in specific models.

Findings

All amplitudes and superpotentials can be computed algorithmically.

Provides a new derivation of the topological metric.

Enables complete description of open topological string amplitudes.

Abstract

Amplitudes in open topological string theory may be described completely by certain A-infinity-categories. We detail a general construction of all cyclic minimal models for a given A-infinity-algebra and apply this result to the case of N=2 supersymmetric Landau-Ginzburg models. This allows to solve the tree-level theory in the sense that all amplitudes and hence the effective superpotential can be computed algorithmically. Furthermore, the construction provides a novel derivation of the topological metric of such models.