D-branes, obstructed curves, and minimal model superpotentials

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.