Introduction to Supersymmetry

TL;DR

The lectures present a thorough, self-contained tour of supersymmetry from 4D representations and superfields to N=1 and N=2 dynamics, holomorphy, and renormalization, culminating in supersymmetry across dimensions 2,6,10, and 11 and their supergravity and string theory connections. The approach blends algebraic structure (central charges, multiplet shortening, automorphisms) with geometric insight (Kähler, special Kähler, hyperkähler manifolds) and nonperturbative dynamics (holomorphy, beta functions, prepotentials, instantons). A central thread is how constraints like holomorphy, R-symmetries, and anomaly cancellation shape the effective actions, moduli spaces, and dualities that underpin modern understanding of gauge theories and quantum gravity. The material thus provides essential tools for exploring dualities, effective actions, and the web of relations linking field theories to string/M-theory.

Abstract

These lectures give a self-contained introduction to supersymmetry from a modern perspective. Emphasis is placed on material essential to understanding duality. Topics include: central charges and BPS-saturated states, supersymmetric nonlinear sigma models, N=2 Yang-Mills theory, holomorphy and the N=2 Yang-Mills beta function, supersymmetry in 2, 6, 10, and 11 spacetime dimensions.