Computation of Superpotentials for D-Branes

TL;DR

This paper introduces a general method to compute tree-level superpotentials for B-type D-branes using A-infinity structures, aiding in understanding D-brane stability and correlation functions in holomorphic Chern-Simons theory.

Contribution

It provides a novel, practical approach to calculating superpotentials for D-branes via A-infinity structures in the derived category of coherent sheaves.

Findings

Rigorous proof of superpotentials for 3-branes on singularities

Application to conifold singularities

New example demonstrating the method's effectiveness

Abstract

We present a general method for the computation of tree-level superpotentials for the world-volume theory of B-type D-branes. This includes quiver gauge theories in the case that the D-brane is marginally stable. The technique involves analyzing the A-infinity structure inherent in the derived category of coherent sheaves. This effectively gives a practical method of computing correlation functions in holomorphic Chern-Simons theory. As an example, we give a more rigorous proof of previous results concerning 3-branes on certain singularities including conifolds. We also provide a new example.