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Fractional Branes and Dynamical Supersymmetry Breaking

Sebastian Franco, Amihay Hanany, Fouad Saad, Angel M. Uranga

TL;DR

We study gauge theories on fractional branes at toric Calabi–Yau singularities and classify their IR dynamics into deformation, N=2, and dynamical SUSY breaking (DSB) sectors.The analysis combines field-theory techniques, brane tilings, and toric-deformation criteria, showing that non-perturbative ADS superpotentials generically drive DSB when supersymmetric flat directions are absent or when FI terms are dynamical ($N_f<N_c$ scenarios are central). Alongside, dynamical FI terms or dibaryons induce runaway directions rather than stable SUSY vacua.These results apply across multiple families (dP1, SPP, higher del Pezzo, and Y^{p,q}) and imply that infrared smoothing of warped throat geometries with 3-form fluxes is unlikely to be achieved by supersymmetric complex deformations; instead, any smoothing would be non-supersymmetric and potentially unstable.Brane tilings provide a practical framework to visualize and compute IR dynamics, connecting rank assignments to beta-function relations and to baryonic U(1) symmetries, thereby clarifying when deformation, N=2, or DSB behavior arises.

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.

Fractional Branes and Dynamical Supersymmetry Breaking

TL;DR

We study gauge theories on fractional branes at toric Calabi–Yau singularities and classify their IR dynamics into deformation, N=2, and dynamical SUSY breaking (DSB) sectors.The analysis combines field-theory techniques, brane tilings, and toric-deformation criteria, showing that non-perturbative ADS superpotentials generically drive DSB when supersymmetric flat directions are absent or when FI terms are dynamical ($N_f<N_c$ scenarios are central). Alongside, dynamical FI terms or dibaryons induce runaway directions rather than stable SUSY vacua.These results apply across multiple families (dP1, SPP, higher del Pezzo, and Y^{p,q}) and imply that infrared smoothing of warped throat geometries with 3-form fluxes is unlikely to be achieved by supersymmetric complex deformations; instead, any smoothing would be non-supersymmetric and potentially unstable.Brane tilings provide a practical framework to visualize and compute IR dynamics, connecting rank assignments to beta-function relations and to baryonic U(1) symmetries, thereby clarifying when deformation, N=2, or DSB behavior arises.

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.

Paper Structure

This paper contains 20 sections, 41 equations, 30 figures.

Table of Contents

  1. Introduction
  2. Classes of fractional branes
  3. The $dP_1$ case
  4. Quiver theory and UV cascade
  5. Dynamical supersymmetry breaking in $dP_1$
  6. Field theory analysis
  7. Analysis in a different regime
  8. Dynamical FI terms
  9. Additional D-brane probes
  10. The SPP example
  11. Higher del Pezzo examples
  12. The $dP_2$ case
  13. The $dP_3$ case
  14. Beyond $dP_3$
  15. The $Y^{p,q}$ family
  16. ...and 5 more sections

Figures (30)

  • Figure 1: Web diagram for the cone over $dP_1$
  • Figure 2: Quiver diagram for the $dP_1$ theory
  • Figure 3: The theory at the end of the duality cascade triggered by $M$ fractional branes. Here labels indicate ranks for the node gauge factors.
  • Figure 4: The quiver for the SPP theory
  • Figure 5: Complex deformation for the SPP theory
  • ...and 25 more figures