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Supersymmetric Actions, Supercurrents, and Quantum Effective Theory

Superspace measures organize supersymmetric interactions, while component reduction reveals their kinetic terms, Yukawa couplings, and scalar potentials. This chapter builds those actions and connects them to quantum effective descriptions and supercurrent multiplets, whose globally allowed improvements carry additional information.

Enter this chapter

Section titled “Enter this chapter”

Begin with Superspace Measures, F-Terms, D-Terms, and Component Extraction to identify the component selected by a superspace integral.

Helpful background. The Action Principle and Field Equations; The 1PI Effective Action and Mean-Field Equations; Current Sources and Generating Functionals provide the variational field equations, the 1PI action, and background current sources used here.

Topics

Section titled “Topics”
  1. Superspace Measures, F-Terms, D-Terms, and Component Extraction — Distinguishes chiral and full-superspace integrals.
  2. Supersymmetric Action Principles and Component Reduction — Checks invariant interactions by component reduction.
  3. Wess–Zumino Models — Builds interacting chiral-multiplet models.
  4. Kähler Sigma Models and Supersymmetric Target Geometry — Relates scalar kinetic terms to Kähler geometry.
  5. Supersymmetric Yang–Mills Actions — Constructs the gauge and gaugino action.
  6. Gauge–Matter Systems, F- and D-Term Potentials, and FI Data — Combines gauging, auxiliary fields, and FI parameters.
  7. Supergraphs, D-Algebra, and Quantum Effective Actions — Separates superspace graph calculations from effective-action interpretation.
  8. Supercurrent Multiplets, Improvements, Anomalies, and Background Sources — Tracks current improvements, anomalies, and background couplings.

How the ideas fit together

Section titled “How the ideas fit together”

A local action can exist even when a particular improved supercurrent multiplet does not exist globally. Improvements shift currents without changing the integrated charges under suitable boundary conditions, but their defining functions must be globally valid. Nontrivial target geometry or FI data can obstruct a preferred improvement, changing which background supergravity multiplet can couple to the theory. Thus component reduction and local conservation laws do not settle every question about global current sources. Komargodski and Seiberg 2010, §§ 2–3.

Where to go next

Section titled “Where to go next”

Continue to Supersymmetric Vacua, Moduli Geometry, and BPS Sectors to solve flatness equations before dividing by genuine gauge redundancy.

References

Section titled “References”
  • Komargodski, Zohar, and Nathan Seiberg. “Comments on Supercurrent Multiplets, Supersymmetric Field Theories and Supergravity.” Journal of High Energy Physics 2010, no. 7 (2010): 017. DOI. Open PDF, arXiv v4.