The DLCQ Spectrum of N=(8,8) Super Yang-Mills

TL;DR

This paper studies the spectrum of 1+1D N=(8,8) super Yang-Mills theory using Discretized Light-Cone Quantization, revealing degeneracies and a mass gap through numerical solutions at finite K.

Contribution

It provides a numerical analysis of the DLCQ spectrum for N=(8,8) super Yang-Mills, preserving supersymmetry and exploring degeneracies and mass gap properties.

Findings

Degeneracies in the spectrum are independent of light-cone compactification.

Numerical results support the existence of a mass gap in the SU(N) theory.

Solutions obtained for K=2,3,4 demonstrate the method's effectiveness.

Abstract

We consider the 1+1 dimensional N = (8,8) supersymmetric matrix field theory obtained from a dimensional reduction of ten dimensional N = 1 super Yang-Mills. The gauge groups we consider are U(N) and SU(N), where N is finite but arbitrary. We adopt light-cone coordinates, and choose to work in the light-cone gauge. Quantizing this theory via Discretized Light-Cone Quantization (DLCQ) introduces an integer, K, which restricts the light-cone momentum-fraction of constituent quanta to be integer multiples of 1/K. Solutions to the DLCQ bound state equations are obtained for K=2,3 and 4 by discretizing the light-cone super charges, which preserves supersymmetry manifestly. We discuss degeneracies in the massive spectrum that appear to be independent of the light-cone compactification, and are therefore expected to be present in the decompactified limit K -> infinity. Our numerical results also support the claim that the SU(N) theory has a mass gap.