Supersymmetry breaking at the end of a cascade of Seiberg dualities

TL;DR

This work analyzes the IR dynamics of a cascading non-conformal quiver gauge theory realized by $N$ regular and $M$ fractional D3-branes at the tip of the complex cone over $dP_1$, whose horizon is $Y^{2,1}$. It demonstrates a self-similar Seiberg duality cascade that preserves the quiver and the form of the superpotential up to couplings, culminating at $N = M$ where the moduli space is quantum-mechanically deformed. The IR analysis shows the generation of an Affleck-Dine-Seiberg superpotential with $W_{ADS}=M\left(\\Lambda^{7M}/\\det\\mathcal{N}\\right)^{1/M}$ and, due to incompatible F-term constraints, absence of a SUSY vacuum, i.e., dynamical SUSY breaking. The results imply a non-supersymmetric deformation of the dual Calabi-Yau cone and point to a broader class of non-AdS/non-CFT dual pairs with broken supersymmetry.

Abstract

We study the IR dynamics of the cascading non-conformal quiver theory on N regular and M fractional D3 branes at the tip of the complex cone over the first del Pezzo surface. The horizon of this cone is the irregular Sasaki-Einstein manifold Y^{2,1}. Our analysis shows that at the end of the cascade supersymmetry is dynamically broken.

Figures (2)

• Figure 1: The non conformal quiver associated to the first del Pezzo surface. Each node represents a gauge factor. Each arrow represents a bi-fundamental chiral multiplet. The chiral fields $X_{41}^\alpha~,~X_{34}^\alpha~,~X_{23}^\alpha$ are doublets with respect to the $SU(2)$ flavor symmetry. The quiver for the conformal case is just the same, with $M=0$.
• Figure 2: The quiver triangle at the bottom of the cascade.