Super Yang-Mills at Weak, Intermediate and Strong Coupling

TL;DR

This paper investigates three-dimensional super-Yang-Mills theory across different coupling regimes, using numerical and analytical methods to analyze bound states and massless states, revealing a transition from particle-like to string-like states at strong coupling.

Contribution

It introduces a supersymmetry-preserving DLCQ regularization and provides a detailed numerical and analytical study of bound and massless states across coupling strengths.

Findings

Bound state masses vary with coupling, showing a transition from weak to strong coupling.

Massless states exist at all couplings, with some becoming string-like at strong coupling.

The regularization preserves supersymmetry during analysis.

Abstract

We consider three dimensional SU(N) N=1 super-Yang-Mills compactified on the space-time R X S^1 X S^1. In particular, we compactify the light-cone coordinate x^- on a light-like circle via DLCQ, and wrap the remaining transverse coordinate on a spatial circle. By retaining only the first few excited modes in the transverse direction, we are able to solve for bound state wave functions and masses numerically by diagonalizing the discretized light-cone supercharge. This regularization of the theory is shown to preserve supersymmetry. We plot bound state masses as a function of the coupling, showing the transition in particle masses as we move from a weakly to a strongly-coupled theory. We analyze both numerically and analytically massless states which exist only in the limit of strong or weak gauge coupling. In addition, we find massless states that persist for all values of the gauge coupling. An analytical treatment of these massless states is provided. Interestingly, in the strong coupling limit, these massless states become string-like.