D-branes, obstructed curves, and minimal model superpotentials

TL;DR

This paper computes superpotentials for D-branes on obstructed rational curves in Calabi-Yau threefolds, revealing an unexpected correspondence with Landau-Ginzburg minimal model superpotentials.

Contribution

It applies Aspinwall-Katz methods to more general obstructed curves, uncovering a novel link to minimal model superpotentials.

Findings

Superpotentials for D-branes on obstructed curves match minimal model superpotentials.

The methods extend previous computations to more complex curve configurations.

An unexpected correspondence between geometric and algebraic models is demonstrated.

Abstract

In this short note we apply methods of Aspinwall-Katz to compute superpotentials of D-branes wrapped on more general obstructed rational curves in Calabi-Yau threefolds. We find an a priori unexpected match between superpotentials from certain such curves and the superpotentials of Landau-Ginzburg models corresponding to minimal models.