Bound States of Dimensionally Reduced {SYM}_{2+1} at Finite N

TL;DR

This paper investigates bound states in dimensionally reduced N=1 SYM in 2+1 dimensions, focusing on finite N, using light-cone formalism, and reveals the superposition nature of SU(N) bound states and the emergence of massless states in DLCQ.

Contribution

It formulates the continuum bound state problem for reduced SYM_{2+1} at finite N in the light-cone framework and analyzes the structure of bound states and massless states.

Findings

SU(N) bound states are superpositions of infinite Fock states

Massless states can arise in DLCQ discretizations

Bound state problem formulated in light-cone formalism

Abstract

We consider the dimensional reduction of N=1 {SYM}_{2+1} to 1+1 dimensions. The gauge groups we consider are U(N) and SU(N), where N is finite. We formulate the continuum bound state problem in the light-cone formalism, and show that any normalizable SU(N) bound state must be a superposition of an infinite number of Fock states. We also discuss how massless states arise in the DLCQ formulation for certain discretizations.