Duality in Supersymmetric Yang-Mills Theory

TL;DR

This paper introduces the behavior of strongly-coupled supersymmetric gauge theories, focusing on effective Lagrangians, nonperturbative effects, and dualities in models like supersymmetric QCD and Seiberg-Witten theory.

Contribution

It provides an overview of nonperturbative phenomena and dualities in supersymmetric Yang-Mills theories, highlighting new insights into their effective actions and geometric descriptions.

Findings

Nonperturbative superpotential generation in supersymmetric QCD

Geometric description of effective coupling in N=2 SU(2) Yang-Mills

Electric-magnetic duality in theories with large N_f

Abstract

These lectures provide an introduction to the behavior of strongly-coupled supersymmetric gauge theories. After a discussion of the effective Lagrangian in nonsupersymmetric and supersymmetric field theories, I analyze the qualitative behavior of the simplest illustrative models. These include supersymmetric QCD for $N_f < N_c$, in which the superpotential is generated nonperturbatively, N=2 SU(2) Yang-Mills theory (the Seiberg-Witten model), in which the nonperturbative behavior of the effective coupling is described geometrically, and supersymmetric QCD for N_f large, in which the theory illustrates a non-Abelian generalization of electric-magnetic duality. [Lectures presented at the 1996 TASI Summer School, to appear in the proceedings.]