Large Volume Perspective on Branes at Singularities

TL;DR

This paper introduces a novel large volume approach to derive worldvolume theories for D3 branes at Calabi-Yau singularities, enabling analysis of complex cases beyond traditional methods.

Contribution

It presents a new extrapolation method for F-term calculations at large volume, allowing derivation of quiver theories for complex singularities with explicit superpotential dependence.

Findings

Derived quiver theories for Del Pezzo surface singularities with multiple exceptional curves.

Superpotentials explicitly depend on complex structure parameters in certain cases.

Method overcomes limitations of traditional approaches for non-toric singularities.

Abstract

In this paper we consider a somewhat unconventional approach for deriving worldvolume theories for D3 branes probing Calabi-Yau singularities. The strategy consists of extrapolating the calculation of F-terms to the large volume limit. This method circumvents the inherent limitations of more traditional approaches used for orbifold and toric singularities. We illustrate its usefulness by deriving quiver theories for D3 branes probing singularities where a Del Pezzo surface containing four, five or six exceptional curves collapses to zero size. In the latter two cases the superpotential depends explicitly on complex structure parameters. These are examples of probe theories for singularities which can currently not be computed by other means.