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Dynamical SUSY Breaking at Meta-Stable Minima from D-branes at Obstructed Geometries

Sebastian Franco, Angel M . Uranga

TL;DR

This work generalizes the ISS mechanism to theories with massless flavors and to quivers on obstructed geometries, showing that meta-stable SUSY-breaking minima can arise when extra massive flavors are added. It develops both field-theoretic models and explicit string-theory embeddings with D7-branes (e.g., in the dP1 setup), including a detailed one-loop analysis that stabilizes pseudomoduli and a parametrically long-lived metastable vacuum. For the simplest obstructed geometry, the complex cone over dP1, the authors demonstrate a local minimum separated from a runaway direction, and they quantify the decay rate via a triangular-barrier bounce action, highlighting the parametric dependence on small flavor masses and extension couplings. The results provide a concrete framework for dynamical SUSY breaking in string-theoretic settings and offer tools (e.g., dimer techniques) to engineer flavored quivers and analyze their stability, with implications for gravity duals and cascades.

Abstract

We study the existence of long-lived meta-stable supersymmetry breaking vacua in gauge theories with massless quarks, upon the addition of extra massive flavors. A simple realization is provided by a modified version of SQCD with N_{f,0} < N_c massless flavors, N_{f,1} massive flavors and additional singlet chiral fields. This theory has local meta-stable minima separated from a runaway behavior at infinity by a potential barrier. We find further examples of such meta-stable minima in flavored versions of quiver gauge theories on fractional branes at singularities with obstructed complex deformations, and study the case of the dP_1 theory in detail. Finally, we provide an explicit String Theory construction of such theories. The additional flavors arise from D7-branes on non-compact 4-cycles of the singularity, for which we find a new efficient description using dimer techniques.

Dynamical SUSY Breaking at Meta-Stable Minima from D-branes at Obstructed Geometries

TL;DR

This work generalizes the ISS mechanism to theories with massless flavors and to quivers on obstructed geometries, showing that meta-stable SUSY-breaking minima can arise when extra massive flavors are added. It develops both field-theoretic models and explicit string-theory embeddings with D7-branes (e.g., in the dP1 setup), including a detailed one-loop analysis that stabilizes pseudomoduli and a parametrically long-lived metastable vacuum. For the simplest obstructed geometry, the complex cone over dP1, the authors demonstrate a local minimum separated from a runaway direction, and they quantify the decay rate via a triangular-barrier bounce action, highlighting the parametric dependence on small flavor masses and extension couplings. The results provide a concrete framework for dynamical SUSY breaking in string-theoretic settings and offer tools (e.g., dimer techniques) to engineer flavored quivers and analyze their stability, with implications for gravity duals and cascades.

Abstract

We study the existence of long-lived meta-stable supersymmetry breaking vacua in gauge theories with massless quarks, upon the addition of extra massive flavors. A simple realization is provided by a modified version of SQCD with N_{f,0} < N_c massless flavors, N_{f,1} massive flavors and additional singlet chiral fields. This theory has local meta-stable minima separated from a runaway behavior at infinity by a potential barrier. We find further examples of such meta-stable minima in flavored versions of quiver gauge theories on fractional branes at singularities with obstructed complex deformations, and study the case of the dP_1 theory in detail. Finally, we provide an explicit String Theory construction of such theories. The additional flavors arise from D7-branes on non-compact 4-cycles of the singularity, for which we find a new efficient description using dimer techniques.

Paper Structure

This paper contains 25 sections, 86 equations, 27 figures.

Table of Contents

  1. Introduction
  2. Meta-stable vacua in $\mathcal{N}=1$ SQCD-like theories with massive and massless flavors
  3. $\mathcal{N}=1$ SQCD with light massive flavors
  4. $\mathcal{N}=1$ SQCD with massless and massive flavors
  5. Extension of SQCD with massless flavors
  6. Review of fractional branes and obstructed deformations
  7. General review of fractional branes
  8. Quiver gauge theories and the ISS proposal
  9. Review of the runaway for fractional branes in the cone over $dP_1$
  10. Flavored $dP_1$
  11. The classical flavored $dP_1$ theory
  12. The local minimum
  13. Behavior at large fields
  14. Lifetime of meta-stable vacua
  15. String theory construction
  16. ...and 10 more sections

Figures (27)

  • Figure 1: A triangular potential barrier.
  • Figure 2: Sketch of the potential along the bounce trajectory and the triangular barrier we use to model it.
  • Figure 3: Quiver diagram for $M$ fractional branes in the complex cone over $dP_1$.
  • Figure 4: Extended quiver diagram for a $dP_1$ theory with flavors.
  • Figure 5: Quiver diagram for the $dP_1$ theory with flavors after dualization. Notice that the number of colors for nodes 1,2 and 3 are $M$, $2M$ and $N_{f,1}-M$. Since D7-branes are mixed after dualization, we represent them with a single white circle.
  • ...and 22 more figures