The Mass Spectrum of N=1 SYM(2+1) at Strong Coupling

TL;DR

This paper computes the mass spectrum of N=1 supersymmetric Yang-Mills theory in 2+1 dimensions at strong coupling using a supersymmetry-preserving numerical approach, revealing stable spectra and massless states.

Contribution

It provides a nonperturbative numerical analysis of the spectrum of N=1 SYM(2+1) at strong coupling using SDLCQ, demonstrating convergence and identifying massless states.

Findings

Mass spectrum converges rapidly with resolution.

Stable spectrum observed at strong coupling.

Identification of two sets of massless states.

Abstract

We consider supersymmetric Yang-Mills theory on R x S^1 x S^1. In particular, we choose one of the compact directions to be light-like and another to be space-like. Since the SDLCQ regularization explicitly preserves supersymmetry, this theory is totally finite, and thus we can solve for bound state wave functions and masses numerically without renormalizing. We present the masses as functions of the longitudinal and transverse resolutions and show that the masses converge rapidly in both resolutions. We also study the behavior of the spectrum as a function of the coupling and find that at strong coupling there is a stable, well defined spectrum which we present. We also find several unphysical states that decouple at large transverse resolution. There are two sets of massless states; one set is massless only at zero coupling and the other is massless at all couplings. Together these sets of massless states are in one-to-one correspondence with the full spectrum of the dimensionally reduced theory.