(1+1)-dimensional large-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>QCD coupled to adjoint fermions

Abstract

We consider (1+1)-dimensional QCD coupled to Majorana fermions in the adjoint representation of the gauge group $\mathrm{SU}(N)$. 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 lightcone Schr\"odinger equation, which we study numerically using the discretized light-cone quantization. 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.