Remarks on quiver gauge theories from open topological string theory

TL;DR

This paper derives quiver gauge theories from Calabi-Yau singularities using open topological string theory, establishing a direct link between string amplitudes and effective superpotentials without effective field theory calculations.

Contribution

It introduces a first-principles approach via open topological string theory to derive quiver gauge theories and superpotentials, connecting string amplitudes with brane tiling results.

Findings

Constructed the A-infinity-structure of open string amplitudes.

Reproduced brane tiling results without effective field theory.

Derived a simple formula for effective superpotentials.

Abstract

We study effective quiver gauge theories arising from a stack of D3-branes on certain Calabi-Yau singularities. Our point of view is a first principle approach via open topological string theory. This means that we construct the natural A-infinity-structure of open string amplitudes in the associated D-brane category. Then we show that it precisely reproduces the results of the method of brane tilings, without having to resort to any effective field theory computations. In particular, we prove a general and simple formula for effective superpotentials.