Dynamics of $SU(N)$ Supersymmetric Gauge Theory

TL;DR

This paper explores the dynamics of $SU(N)$ supersymmetric gauge theories, analyzing their solutions, phase structures, and behaviors in the large $N$ limit, revealing complex phenomena like confinement, spectrum features, and mass hierarchies.

Contribution

It provides exact results on the crossover from weak to strong coupling, identifies a scaling regime with surviving instanton effects, and discusses the implications for large $N$ confining theories.

Findings

Identification of a scaling regime with light W bosons

Exact results for the weak to strong coupling crossover

Large hierarchy of mass scales in the scaling regime

Abstract

We study the physics of the Seiberg-Witten and Argyres-Faraggi-Klemm-Lerche-Theisen-Yankielowicz solutions of $D=4$, $\mathcal{N}=2$ and $\mathcal{N}=1$ $SU(N)$ supersymmetric gauge theory. The $\mathcal{N}=1$ theory is confining and its effective Lagrangian is a spontaneously broken $U(1)^{N-1}$ abelian gauge theory. We identify some features of its physics which see this internal structure, including a spectrum of different string tensions. We discuss the limit $N\rightarrow\infty$, identify a scaling regime in which instanton and monopole effects survive, and give exact results for the crossover from weak to strong coupling along a scaling trajectory. We find a large hierarchy of mass scales in the scaling regime, including very light $W$ bosons, and the absence of weak coupling. The light $W$'s leave a novel imprint on the effective dual magnetic theory. The effective Lagrangian appears to be inadequate to understand the conventional large $N$ limit of the confining $\mathcal{N}=1$ theory.