David Tong: Supersymmetry

David Tong: Lectures on Supersymmetry

This is a course of supersymmetric field theory given to Part III (i.e. masters level) students. It covers the basics of supersymmetric field theories, as well as more advanced topics such as Seiberg duality. Please do email me if you find any typos or mistakes.



  • 1. Introduction:   PDF
    Table of Contents. Why study supersymmetry?
  • 2. The Supersymmetry Algebra:   PDF
    The Lorentz group, spinors and SL(2,C), The Poincare group. The supersymmetry algebra, R-symmetry. Representations of the Poincare group and the susy algebra. Extended supersymmetry and BPS states.
  • 3. Chiral Superfields:   PDF
    Superspace and superfields. Chiral superfields. F-terms and D-terms. The Wess-Zumino model, non-linear sigma models. Non-renormalisation theorems and the power of holomorphy. Supersymmetry breaking, the Goldstino, the Witten index, the O'Raifeartaigh model, the Nelson-Seiberg argument.
  • 4. Supersymmetric Gauge Theories:   PDF
    Real superfields and the field strength. Supersymmetric QED, Super Yang-Mills and SQCD. The moduli space of vacua, gauged linear models. Extended supersymmetry.
  • 5. Boot Camp: Quantum Gauge Dynamics:   PDF
    The beta function and strong coupling; Confinement and the mass gap; Chiral symmetry breaking; Phases of massless QCD. Gauge anomalies, chiral anomalies, and 't Hooft anomalies; Instantons.
  • 6. Supersymmetric QCD:   PDF
    Super Yang-Mills, confinement and chiral symmetry breaking, the Witten index. Symmetries of SQCD and a runaway potential. More on SQCD: a deformed moduli space, 't Hooft anomaly matching, and confinement without chiral symmetry breaking. The conformal window and superconformal field theories. Seiberg duality.
  • 7. More Supersymmetric Gauge Dynamics:   PDF
    Other gauge groups and Intriligator-Pouliot duality; Chiral gauge theories and Pouliot-Strassler duality; a-maximization. Dynamical supersymmetry breaking.

Problem Sheets

  • Problem Sheet 1:   PDF    Spinors and Superspace.

  • Problem Sheet 2:   PDF    Non-Renormalisation Theorems. Susy Gauge Theories.

  • Problem Sheet 3:   PDF    Quantum Gauge Dynamics.

  • Problem Sheet 4:   PDF    SQCD.

Supersymmetry on the Web

The Basics and More

Supersymmetry Breaking

N=1 Dualities