Dynamics of $SU(N)$ Supersymmetric Gauge Theory

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 $N\to \infty$, 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.

Comments: 28 pages, harvmac, 4 eps figures in separate uuencoded file. We have extended this paper considerably, adding new results, discussion and figures. In particular, we give exact formulas for masses and couplings along a scaling trajectory appropriate to the large $N$ limit. These formulas display a novel effect due to light electric $W$ bosons down to energy scales $\sim e^{-N}$, deep in the weak coupling magnetic regime