Subtleties in QCD theory in Two Dimensions

Abstract

It is shown that in a formulation of Yang-Mills theory in two dimensions in terms of $A=if^{-1}\pa f$, $\bar A=i\bar f\bpa\bar f^{-1}$ with $f(z,\bar{z})$, $\bar{f}(z,\bar{z})\in [SU(N_C){]}^c$ the complexification of $SU(N_C)$ , reveals certain subtleties. ``Physical" massive color singlet states seem to exist. When coupled to $N_F$ quarks the coupling constant is renormalized in such a way that it vanishes for the pure Yang- Mills case. This renders the above states massless and unphysical. In the abelian case, on the other hand, the known results of the Schwinger model are reproduced with no need of such a renormalization. The massless $QC{D}_2$ theory is analyzed in similar terms and peculiar massive states appear, with a mass of $e_c\sqrt{\frac{N_F}{2\pi }}$.

21 pages

References in corpus (6)

• Equivalence of Two Dimensional QCD and the $c=1$ Matrix Model
• Bosonization and QCD in Two Dimensions
• Quark solitons as constituents of hadrons
• Physical States in G/G Models and 2d Gravity
• G/G Models and W_N strings
• On the twisted G/H topological models

Cited by in corpus (12)

• Mesonic Spectra of Bosonized QCD_2 Models
• Anomalous Soft Photons in Hadron Production
• The spectrum of multi-flavor QCD_2 and the non-Abelian Schwinger equation
• QCD2-Screening, Confinement and Novel non-abelian Solutions
• Adjoint QCD2 and the Non-Abelian Schwinger Mechanism
• The Wigner Function of Produced Particles in String Fragmentation
• The spectrum of states with one current acting on the adjoint vacuum of massless QCD2
• The Adjoint Vacuum Sector of Massless QCD2
• The Compactification of QCD${}_4$ to QCD${}_2$ in a Flux Tube
• On the question of quark confinement in the Abelian U(1) QED gauge interaction
• Classical integrability of chiral $QC{D}_2$ and classical curves
• Event-by-Event Study of Space-Time Dynamics in Flux-Tube Fragmentation