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N=1 Duality, RG Fixed Points, and Protected SCFT Data

Seiberg duality links different ultraviolet theories through a common infrared description. This chapter tests that proposal using operators, anomalies, and deformations, then asks what superconformal R-symmetry and protected data can determine once an interacting fixed point is justified.

Enter this chapter

Section titled “Enter this chapter”

Begin with Seiberg Duality in SQCD to write the electric and magnetic SQCD theories in compatible conventions.

Helpful background. Ultraviolet and Infrared Fixed Points: Criteria and Evidence; Unitarity Bounds and Null States; ‘t Hooft Anomaly Matching provide the fixed-point criteria, unitarity bounds, and anomaly matching used here.

Topics

Section titled “Topics”
  1. Seiberg Duality in SQCD — States the dual pair and its infrared regime.
  2. Operator Dictionaries, Chiral Rings, and Anomaly Matching — Matches chiral operators and anomaly coefficients.
  3. Mass Deformations, Higgsing, and Dual RG Flows — Checks compatible endpoints under masses and Higgs expectation values.
  4. The Conformal Window and Interacting Fixed Points — Separates interacting, free, and confining regimes.
  5. Accidental Symmetries and a-Maximization — Includes accidental currents when determining the exact R-symmetry.
  6. Conformal Manifolds and Duality Actions — Distinguishes exactly marginal directions from generic couplings.
  7. Protected N=1 SCFT Data and the Bootstrap Export — Translates protected data without supplying unprotected crossing information.
  8. Emergent and Non-Lagrangian N=1 Descriptions — States what supports a theory without a known weakly coupled Lagrangian.

How the ideas fit together

Section titled “How the ideas fit together”

An anomaly-free trial R-current may mix with flavor currents. At a suitable four-dimensional N=1 fixed point, a-maximization selects the superconformal combination, but an operator reaching a unitarity bound can become free and introduce an accidental symmetry. Ignoring that current gives the wrong optimization problem. Matching the resulting protected quantities supports the duality in the stated regime, while full correlator dynamics remains additional information. Intriligator and Wecht 2003, §§ 1–2.4.

Where to go next

Section titled “Where to go next”

Continue to N=2 Gauge Dynamics and Seiberg–Witten Geometry to identify the multiplets and vacuum branches of an N=2 theory.

References

Section titled “References”
  • Intriligator, Kenneth, and Brian Wecht. “The Exact Superconformal R-Symmetry Maximizes aa.” Nuclear Physics B 667 (2003): 183–200. arXiv:hep-th/0304128.