Matrix Factorizations and Homological Mirror Symmetry on the Torus

TL;DR

This paper explores matrix factorizations and homological mirror symmetry on the torus using Landau-Ginzburg models, identifying key factorizations, computing spectra, and verifying mirror symmetry through three-point functions.

Contribution

It provides a detailed analysis of matrix factorizations on the torus and confirms homological mirror symmetry by explicit spectrum and correlator calculations.

Findings

Identified basic matrix factorizations of the superpotential

Computed the full spectrum including moduli dependence

Verified homological mirror symmetry via three-point functions

Abstract

We consider matrix factorizations and homological mirror symmetry on the torus T^2 using a Landau-Ginzburg description. We identify the basic matrix factorizations of the Landau-Ginzburg superpotential and compute the full spectrum, taking into account the explicit dependence on bulk and boundary moduli. We verify homological mirror symmetry by comparing three-point functions in the A-model and the B-model.