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Supersymmetry Breaking and Controlled Deformations

Supersymmetry breaking can be spontaneous, metastable, nonlinearly realized at low energy, or introduced explicitly by soft terms. This chapter distinguishes these possibilities using auxiliary-field equations, the goldstino, loop-lifted flat directions, and decay or decoupling tests.

Enter this chapter

Section titled “Enter this chapter”

Begin with F- and D-Term Breaking, Vacuum Energy, and the Goldstino to relate nonzero auxiliary fields to vacuum energy and the goldstino.

Helpful background. Bounce Solutions and False-Vacuum Boundary Conditions; Power Counting and Predictive Order; Ultraviolet and Infrared Fixed Points: Criteria and Evidence provide the bounce calculations, effective-theory counting, and fixed-point limitations used here.

Topics

Section titled “Topics”
  1. F- and D-Term Breaking, Vacuum Energy, and the Goldstino — Tests spontaneous breaking in a positive-metric rigid theory.
  2. O’Raifeartaigh and Fayet–Iliopoulos Model Laboratories — Solves explicit F- and D-term model examples.
  3. R-Symmetry and Nelson–Seiberg-Type Criteria — States the hypotheses of R-symmetry criteria.
  4. Pseudomoduli, Quantum Lifting, and Metastability — Determines whether quantum corrections stabilize a local minimum.
  5. Nonlinear Goldstino Dynamics and Constrained Effective Theory — Builds a goldstino EFT after heavy partners decouple.
  6. Soft Breaking, Spurions, and Controlled Decoupling — Tracks explicit soft operators and their controlled limits.

How the ideas fit together

Section titled “How the ideas fit together”

Incompatible F-flatness equations can establish nonzero vacuum energy without establishing a stable vacuum: a flat direction may run away or acquire an unstable quantum correction. A loop calculation can instead produce a local minimum whose lifetime still requires a tunneling analysis. At energies below the remaining massive excitations, the goldstino realizes broken supersymmetry nonlinearly; this low-energy description does not prove global stability. R-symmetry criteria and auxiliary-field tests must therefore be combined with the actual potential and its domain of control. Intriligator, Seiberg, and Shih 2006, §§ 2–3.

Where to go next

Section titled “Where to go next”

Continue to Four-Dimensional N=1 Gauge Dynamics to specify SQCD matter, symmetries, and classical vacuum coordinates.

References

Section titled “References”
  • Intriligator, K., N. Seiberg, and D. Shih. “Dynamical SUSY Breaking in Meta-Stable Vacua.” Journal of High Energy Physics 2006, no. 04 (2006): 021. DOI. Open preprint.