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TASI-2002 Lectures: Non-perturbative Supersymmetry

John Terning

TL;DR

This collection of lectures surveys non-perturbative results in N=1 SUSY gauge theories rooted in holomorphy and Seiberg duality, with emphasis on applications to dynamical SUSY breaking. It develops the holomorphic structure of couplings and superpotentials, analyzes anomalies and instantons, and uses ADS superpotentials and gaugino condensation to understand vacuum structure. A central theme is the emergence of dual descriptions (Seiberg duality) and their infrared fixed points, confinement patterns (including S-confinement), and the role of anomalies in guiding consistent IR physics. The material connects non-perturbative dynamics to gauge mediation and dynamical SUSY breaking, highlighting how holomorphy and duality provide powerful tools for predicting IR behavior in strongly coupled theories.

Abstract

These lectures contain a pedagogical review of non-perturbative results from holomorphy and Seiberg duality with applications to dynamical SUSY breaking. Background material on anomalies, instantons, unitarity bounds from superconformal symmetry, and gauge mediation are also included.

TASI-2002 Lectures: Non-perturbative Supersymmetry

TL;DR

This collection of lectures surveys non-perturbative results in N=1 SUSY gauge theories rooted in holomorphy and Seiberg duality, with emphasis on applications to dynamical SUSY breaking. It develops the holomorphic structure of couplings and superpotentials, analyzes anomalies and instantons, and uses ADS superpotentials and gaugino condensation to understand vacuum structure. A central theme is the emergence of dual descriptions (Seiberg duality) and their infrared fixed points, confinement patterns (including S-confinement), and the role of anomalies in guiding consistent IR physics. The material connects non-perturbative dynamics to gauge mediation and dynamical SUSY breaking, highlighting how holomorphy and duality provide powerful tools for predicting IR behavior in strongly coupled theories.

Abstract

These lectures contain a pedagogical review of non-perturbative results from holomorphy and Seiberg duality with applications to dynamical SUSY breaking. Background material on anomalies, instantons, unitarity bounds from superconformal symmetry, and gauge mediation are also included.

Paper Structure

This paper contains 55 sections, 473 equations, 4 figures.

Table of Contents

  1. Holomorphy
  2. Non-renormalization Theorems
  3. Wavefunction Renormalization
  4. Integrating Out
  5. The Holomorphic Gauge Coupling
  6. Review of Anomalies and Instantons
  7. Anomalies in the Path Integral
  8. Gauge Anomalies
  9. Review of Instantons
  10. Instantons in Broken Gauge Theories
  11. Gaugino Condensation
  12. The Affleck-Dine-Seiberg Superpotential
  13. Symmetry and Holomorphy
  14. Consistency of $W_{\rm ADS}$: Moduli Space
  15. Consistency of $W_{\rm ADS}$: Mass Perturbations
  16. ...and 40 more sections

Figures (4)

  • Figure 1: The fermion triangle which contributes to the anomaly. One also adds the crossed graph where the gauge bosons are interchanged.
  • Figure 2: Instanton with 2N-2 quark legs (solid, straight lines) and 2N gaugino legs (wavy lines), connected by 2N squark VEVs (dashed lines with crosses).
  • Figure 3: Squark VEV (dashed line with cross) gives a mass to a quark (solid lines) and a gaugino (wavy line).
  • Figure 4: Instanton contribution to the interaction between two mesinos (external straight lines) and $N-1$ mesons (dash-dot lines). The instanton has 4 gaugino legs (internal wavy lines) and $N+2$ quark and anti-quark legs (internal straight lines). A squark VEV and an anti-squark VEV are shown (dashed line with cross) gives a mass to a quark and a gaugino or a anti-quark and gaugino, however they can be arbitrarily many insertions of these VEVs which must be re-summed.