Supersymmetric Theory and Models

TL;DR

This paper provides an introductory overview of supersymmetric theories, covering their mathematical foundations, model construction, symmetry breaking mechanisms, and the formulation of the MSSM, with implications for particle physics.

Contribution

It systematically introduces supersymmetry, superspace formalism, gauge theories, SUSY-breaking mechanisms, and the MSSM, offering a comprehensive beginner-friendly review.

Findings

Introduction of two-component spinors for fermions

Construction of the MSSM and its implications

Discussion of SUSY-breaking mechanisms

Abstract

In these introductory lectures, we review the theoretical tools used in constructing supersymmetric field theories and their application to physical models. We first introduce the technology of two-component spinors, which is convenient for describing spin-$1/2$ fermions. After motivating why a theory of nature may be supersymmetric at the TeV energy scale, we show how supersymmetry (SUSY) arises as an extension of the Poincar\'e algebra of spacetime symmetries. We then obtain the representations of the SUSY algebra and discuss its simplest realization in the Wess-Zumino model. In order to have a systematic approach for obtaining supersymmetric Lagrangians, we introduce the formalism of superspace and superfields and recover the Wess-Zumino Lagrangian. These methods are then extended to encompass supersymmetric abelian and non-abelian gauge theories coupled to supermatter. Since supersymmetry is not an exact symmetry of nature, it must ultimately be broken. We discuss several mechanisms of SUSY-breaking (both spontaneous and explicit) and briefly survey various proposals for realizing SUSY-breaking in nature. Finally, we construct the the Minimal Supersymmetric extension of the Standard Model (MSSM), and consider the implications for the future of SUSY in particle physics.