Symmetry and fields on the walk into the Cambridge maths department.
Supersymmetric Field Theory
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.
Introduction
Table of Contents. Why study supersymmetry?
The Supersymmetry Algebra
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.
Chiral Superfields
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.
Supersymmetric Gauge Theories
Real superfields and the field strength. Supersymmetric QED, Super Yang-Mills and SQCD. The moduli space of vacua, gauged linear models. Extended supersymmetry.
Boot Camp: Quantum Gauge Dynamics
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.
Supersymmetric QCD
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.
More Supersymmetric Gauge Dynamics
Other gauge groups and Intriligator-Pouliot duality; Chiral gauge theories and Pouliot-Strassler duality; a-maximization. Dynamical supersymmetry breaking.