On the spectrum of(1+1)-dimensional QCD withSU(Nc)currents

Abstract

Extending previous work, we calculate the fermionic spectrum of two-dimensional QCD $({\mathrm{QCD}}_{2})$ in the formulation with ${SU(N}_{c})$ currents. Together with the results in the bosonic sector this allows us 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, $\ensuremath{\lambda}{=N}_{f}{/N}_{c},$ anew. We construct the Hamiltonian matrix in the DLCQ formulation as an algebraic function of the harmonic resolution K and the continuous parameter \ensuremath{\lambda} in the Veneziano limit. We find that the fermion momentum is a function of \ensuremath{\lambda} in the discrete approach. A universality, existing only in two dimensions, dictates that the well-known 't Hooft and large ${N}_{f}$ spectra be reproduced in the limits $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\lambda}}0$ and \ensuremath{\infty}, which we confirm. We identify their single-particle content which is surprisingly the same as in the bosonic sectors. All multiparticle states are classified in terms of their constituents. These findings allow for an identification of the lowest single particles of the adjoint theory. While we do not succeed in interpreting this spectrum completely, evidence is presented for the conjecture that adjoint ${\mathrm{QCD}}_{2}$ has a bosonic and an independent fermionic Regge trajectory of single-particle states.