Exact Symmetries and Threshold States in Two-Dimensional Models for QCD

TL;DR

This paper explores the spectrum of a two-dimensional SU(N) gauge theory with fermions, revealing exact symmetries, degeneracies, and the continuum nature of meson spectra, providing insights into the model's threshold states and string tension behavior.

Contribution

It uncovers exact symmetry algebras and degeneracies in the meson spectrum of 2D QCD-like models, extending previous studies with new analytical and numerical results.

Findings

Exact osp(1|4) symmetry leads to degeneracies in the massless case.

Many states are threshold bound states degenerate with multi-trace states.

The meson spectrum becomes continuous above a certain threshold when quarks are massive.

Abstract

Two-dimensional SU$(N)$ gauge theory coupled to a Majorana fermion in the adjoint representation is a nice toy model for higher-dimensional gauge dynamics. It possesses a multitude of "gluinoball" bound states whose spectrum has been studied using numerical diagonalizations of the light-cone Hamiltonian. We extend this model by coupling it to $N_f$ flavors of fundamental Dirac fermions (quarks). The extended model also contains meson-like bound states, both bosonic and fermionic, which in the large-$N$ limit decouple from the gluinoballs. We study the large-$N$ meson spectrum using the Discretized Light-Cone Quantization (DLCQ). When all the fermions are massless, we exhibit an exact $\mathfrak{osp}(1|4)$ symmetry algebra that leads to an infinite number of degeneracies in the DLCQ approach. More generally, we show that many single-trace states in the theory are threshold bound states that are degenerate with multi-trace states. These exact degeneracies can be explained using the Kac-Moody algebra of the SU$(N)$ current. We also present strong numerical evidence that additional threshold states appear in the continuum limit. Finally, we make the quarks massive while keeping the adjoint fermion massless. In this case too, we observe some exact degeneracies that show that the spectrum of mesons becomes continuous above a certain threshold. This demonstrates quantitatively that the fundamental string tension vanishes in the massless adjoint QCD$_2$.