DLCQ Bound States of N =(2,2) Super-Yang-Mills at Finite and Large N

TL;DR

This paper uses Discretized Light-Cone Quantization to analyze bound states in 1+1 dimensional N=(2,2) super-Yang-Mills theory, revealing massless states and a string-like spectrum at large N.

Contribution

It provides numerical solutions for bound states at finite K, demonstrating the existence of massless states and supporting the theory's screening phase.

Findings

Existence of normalizable massless states as K approaches infinity

Spectrum dominated by string-like or many parton states

No evidence of a mass gap in the continuum limit

Abstract

We consider the 1+1 dimensional N = (2,2) supersymmetric matrix model which is obtained by dimensionally reducing N = 1 super Yang-Mills from four to two dimensions. The gauge groups we consider are U(Nc) and SU(Nc), where Nc 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,...,6 by discretizing the light-cone supercharges, which results in a supersymmetric spectrum. Our numerical results imply the existence of normalizable massless states in the continuum limit K -> infinity, and therefore the absence of a mass gap. The low energy spectrum is dominated by string-like (or many parton) states. Our results are consistent with the claim that the theory is in a screening phase.