Supersymmetry Breaking from a Calabi-Yau Singularity

TL;DR

This paper proposes a geometric criterion to determine when supersymmetry is spontaneously broken in string backgrounds involving Calabi-Yau singularities with wrapped branes, supported by an example analysis of a specific quiver gauge theory.

Contribution

It introduces a conjecture linking Calabi-Yau singularity obstructions to supersymmetry breaking, supported by a detailed example analysis of the $Y^{2,1}$ quiver gauge theory.

Findings

Gaugino condensation leads to a deformation of the chiral ring with no solutions.

Supersymmetry breaking occurs when the number of deformations is less than the fractional branes.

The criterion is expected to be general for singularities with limited deformations.

Abstract

We conjecture a geometric criterion for determining whether supersymmetry is spontaneously broken in certain string backgrounds. These backgrounds contain wrapped branes at Calabi-Yau singularites with obstructions to deformation of the complex structure. We motivate our conjecture with a particular example: the $Y^{2,1}$ quiver gauge theory corresponding to a cone over the first del Pezzo surface, $dP_1$. This setup can be analyzed using ordinary supersymmetric field theory methods, where we find that gaugino condensation drives a deformation of the chiral ring which has no solutions. We expect this breaking to be a general feature of any theory of branes at a singularity with a smaller number of possible deformations than independent anomaly-free fractional branes.