On the Spectrum of QCD(1+1) with SU(N_c) Currents

TL;DR

This paper calculates the fermionic spectrum of two-dimensional QCD with SU(N_c) currents, revealing how the spectrum depends on the ratio of flavors to colors and connecting fermionic and bosonic sectors.

Contribution

It extends previous work by deriving the fermionic spectrum in QCD_2 with SU(N_c) currents and analyzing its dependence on the flavor-color ratio , providing new insights into the single-particle states.

Findings

Fermion momentum depends on , matching known spectra.

Fermionic and bosonic sectors share the same single-particle content.

Large differences in Fock space sizes between sectors enable state interpretation.

Abstract

Extending previous work, we calculate in this note the fermionic spectrum of two-dimensional QCD (QCD_2) in the formulation with SU(N_c) currents. Together with the results in the bosonic sector this allows to address the as yet unresolved task of finding the single-particle states of this theory as a function of the ratio of the numbers of flavors and colors, \lambda=N_f/N_c, anew. We construct the Hamiltonian matrix in DLCQ formulation as an algebraic function of the harmonic resolution K and the continuous parameter \lambda. Amongst the more surprising findings in the fermionic sector chiefly considered here is that the fermion momentum is a function of \lambda. This dependence is necessary in order to reproduce the well-known 't Hooft and large N_f spectra. Remarkably, those spectra have the same single-particle content as the ones in the bosonic sectors. The twist here is the dramatically different sizes of the Fock bases in the two sectors, which makes it possible to interpret in principle all states of the discrete approach. The hope is that some of this insight carries over into the continuum. We also present some new findings concerning the single-particle spectrum of the adjoint theory.