Fractional Branes and Dynamical Supersymmetry Breaking

TL;DR

This paper investigates the dynamics of fractional branes at toric singularities, revealing that they often lead to dynamical supersymmetry breaking with runaway behavior, and discusses implications for dual geometries and brane tilings.

Contribution

It provides a comprehensive analysis of fractional branes at various toric singularities, including new insights into supersymmetry breaking and dual geometric interpretations.

Findings

Most fractional branes induce dynamical supersymmetry breaking.

Special cases recover supersymmetric IR behaviors like confinement or N=2 theories.

In supersymmetry breaking cases, theories exhibit runaway behavior involving moduli.

Abstract

We study the dynamics of fractional branes at toric singularities, including cones over del Pezzo surfaces and the recently constructed Y^{p,q} theories. We find that generically the field theories on such fractional branes show dynamical supersymmetry breaking, due to the appearance of non-perturbative superpotentials. In special cases, one recovers the known cases of supersymmetric infrared behaviors, associated to SYM confinement (mapped to complex deformations of the dual geometries, in the gauge/string correspondence sense) or N=2 fractional branes. In the supersymmetry breaking cases, when the dynamics of closed string moduli at the singularity is included, the theories show a runaway behavior (involving moduli such as FI terms or equivalently dibaryonic operators), rather than stable non-supersymmetric minima. We comment on the implications of this gauge theory behavior for the infrared smoothing of the dual warped throat solutions with 3-form fluxes, describing duality cascades ending in such field theories. We finally provide a description of the different fractional branes in the recently introduced brane tiling configurations.