A Crash Course in Supersymmetric Field Theory Across Dimensions

Abstract

These notes give a cross-dimensional crash course in supersymmetric field theory. The goal is to provide enough common language to recognize the basic setups used in talks and papers, while also working through representative computations that make the terminology concrete. We begin with supersymmetry algebras, multiplets, protected quantities, moduli spaces, deformations, and anomalies, then follow these ideas through examples in two to ten spacetime dimensions. The emphasis is on recurring structures, such as holomorphy, supersymmetric vacua, dualities, extremization principles, indices, BPS data, and anomaly constraints, rather than on a classification of theories in any one dimension.