On Matrix Factorizations, Residue Pairings and Homological Mirror Symmetry

TL;DR

This paper demonstrates how boundary B-type Landau-Ginzburg models with matrix factorizations can compute exact superpotentials and disk instanton corrections in Calabi-Yau spaces, linking algebraic structures to Gromov-Witten invariants.

Contribution

It introduces a differential equation involving matrix Saito's higher residue pairings to compute open-string correlators and Gromov-Witten invariants in Calabi-Yau geometries.

Findings

Computed quantum products m_2 and m_3 for elliptic curves

Reproduced boundary changing open Gromov-Witten invariants

Linked matrix factorizations to mirror symmetry and instanton corrections

Abstract

We argue how boundary B-type Landau-Ginzburg models based on matrix factorizations can be used to compute exact superpotentials for intersecting D-brane configurations on compact Calabi-Yau spaces. In this paper, we consider the dependence of open-string, boundary changing correlators on bulk moduli. This determines, via mirror symmetry, non-trivial disk instanton corrections in the A-model. As crucial ingredient we propose a differential equation that involves matrix analogs of Saito's higher residue pairings. As example, we compute from this for the elliptic curve certain quantum products m_2 and m_3, which reproduce genuine boundary changing, open Gromov-Witten invariants.