On Stable Non-Supersymmetric Vacua at the Bottom of Cascading Theories

TL;DR

The paper investigates cascading ${ m SU}(N)$ quiver gauge theories arising from fractional branes at toric del Pezzo cones and shows that IR runaway behavior can be stabilized into stable non-supersymmetric vacua by specific baryonic deformations of the bottom-tree-level superpotential. Stable DSB vacua appear only in tightly constrained setups, notably for $dP_1$ with a single fractional brane ($M=1$), and for $dP_2$ (and similarly in $dP_3$) when a small number of SB branes are present alongside many deformation branes, with a corresponding KS-like background emerging in the large deformation-brane limit. Contrastingly, infinite families like the $Y^{p,q}$ and $X^{p,q}$ do not generally admit such stabilization, indicating a restricted pattern tied to del Pezzo geometries. The work suggests a broadly applicable, holographically tractable pattern for DSB in cascading quivers and points to future string-theory realizations of the necessary baryonic deformations and their gravity duals, as well as possible phenomenological insights from probe-brane dynamics.

Abstract

We consider a wide class of cascading gauge theories which usually lead to runaway behaviour in the IR, and discuss possible deformations of the superpotential at the bottom of the cascade which stabilize the runaway direction and provide stable non-supersymmetric vacua. The models we find may allow for a weakly coupled supergravity analysis of dynamical supersymmetric breaking in the context of the gauge/string correspondence.

Figures (8)

• Figure 1: Quiver of the $dP_1$ theory for $M$ fractional branes.
• Figure 2: Quiver of the $dP_1$ theory for one fractional brane. The dashed node represents an "SU(1)" factor, which plays no rôle in the IR.
• Figure 3: Quiver of the $dP_2$ theory for generic $P$ and $K$.
• Figure 4: Quiver of the $dP_2$ theory for generic $K$ and $P=0$.
• Figure 5: Quiver of the $dP_2$ theory for generic $P$ and $K=1$. The dashed node represents an "SU(1)" factor, which plays no rôle in the IR.