D-brane Moduli Spaces and Superpotentials in a Two-Parameter Model

TL;DR

This paper investigates the moduli spaces and superpotentials of D2-branes on a specific K3-fibration using matrix factorizations, revealing complex intersecting branches and the effects of non-toric deformations.

Contribution

It provides a detailed analysis of D2-brane moduli spaces and superpotentials in a two-parameter model using Landau-Ginzburg techniques, including the role of non-toric deformations.

Findings

Open string moduli space has intersecting branches of varying dimensions.

Families of D2-branes intersect with bound state branches.

Non-toric complex structure deformations influence the moduli space.

Abstract

We study D2-branes on the K3-fibration P^4_(11222)[8] using matrix factorizations at the Landau-Ginzburg point and analyze their moduli space and superpotentials in detail. We find that the open string moduli space consists of various intersecting branches of different dimensions. Families of D2-branes wrapping rational curves of degree one intersect with bound state branches. The influence of non-toric complex structure deformations is investigated in the Landau-Ginzburg framework, where these deformations arise as bulk moduli from the twisted sectors.