$1+1$-Dimensional Large $N$ QCD coupled to Adjoint Fermions

TL;DR

This paper analyzes 1+1-dimensional large N QCD with adjoint fermions, revealing a discrete spectrum of bound states with complex wave functions, using numerical light-cone quantization methods.

Contribution

It provides a numerical study of the spectrum of large N QCD with adjoint fermions, showing the structure of bound states and their wave functions.

Findings

Discrete spectrum of bound states identified

Logarithmic growth of level density with mass

Low-lying states close to fixed parton number eigenstates

Abstract

We consider 1+1-dimensional QCD coupled to Majorana fermions in the adjoint representation of the gauge group $SU(N)$. Pair creation of partons (fermion quanta) is not suppressed in the large-$N$ limit, where the glueball-like bound states become free. In this limit the spectrum is given by a linear \lc\ Schr\" odinger equation, which we study numerically using the discretized \lcq. We find a discrete spectrum of bound states, with the logarithm of the level density growing approximately linearly with the mass. The wave function of a typical excited state is a complicated mixture of components with different parton numbers. A few low-lying states, however, are surprisingly close to being eigenstates of the parton number, and their masses can be accurately calculated by truncated diagonalizations.