N=1 super Yang-Mills on a (3+1) dimensional transverse lattice with one exact supersymmetry

TL;DR

This paper formulates N=1 super Yang-Mills theory on a transverse lattice in 3+1 dimensions, preserving one supersymmetry, and analyzes its mass spectrum and phase transition behavior in the large-Nc limit.

Contribution

It introduces a supersymmetric lattice formulation of N=1 super Yang-Mills in 3+1 dimensions that preserves one supersymmetry and explores its non-perturbative mass spectrum.

Findings

Rich, non-trivial mass spectrum behavior as a function of coupling.

Evidence of a transition in bound state structure from weak to strong coupling.

Mass spectrum fits with string theory justified model are preferred.

Abstract

We formulate ${\cal N}$=1 super Yang-Mills theory in 3+1 dimensions on a two dimensional transverse lattice using supersymmetric discrete light cone quantization in the large-$N_c$ limit. This formulation is free of fermion species doubling. We are able to preserve one supersymmetry. We find a rich, non-trivial behavior of the mass spectrum as a function of the coupling $g\sqrt{N_c}$, and see some sort of "transition" in the structure of a bound state as we go from the weak coupling to the strong coupling. Using a toy model we give an interpretation of the rich behavior of the mass spectrum. We present the mass spectrum as a function of the winding number for those states whose color flux winds all the way around in one of the transverse directions. We use two fits to the mass spectrum and the one that has a string theory justification appears preferable. For those states whose color flux is localized we present an extrapolated value for $m^2$ for some low energy bound states in the limit where the numerical resolution goes to infinity.