Mesonic Spectra of Bosonized QCD_2 Models

We discuss bosonized two-dimensional QCD with massless fermions in the adjoint and multi-flavor fundamental representations. We evaluate the massive mesonic spectra of several models by using the light-front quantization and diagonalizing the mass operator $M^2=2P^+P^-$. We recover previous results in the case of one flavor adjoint fermions and we find the exact massive spectrum of multi flavor QCD in the limit of large number of flavors.Comment: 17 pages, Late

The string tension in massive QCD2QCD_2

We compute the string tension in massive $QCD_2$. It is shown that the string tension vanishes when the mass of the dynamical quark is zero, with no dependence on the representations of the dynamical or of the external charges. When a small mass ($m\ll e$) is added, a tension appears and we calculate its value as a function of the representations.Comment: 10 pages, Late

Screening and confinement in large N_f QCD_2 and in N=1 SYM_2

The screening nature of the potential between external quarks in massless $SU(N_c)$ $QCD_2$ is derived using an expansion in $N_f$- the number of flavors. Applying the same method to the massive model, we find a confining potential. We consider the N=1 super Yang Mills theory, reveal certain problematic aspects of its bosonized version and show the associated screening behavior by applying a point splitting method to the scalar current.Comment: 23 pages, Latex. 1 figur

The spectrum of multi-flavor QCD_2 and the non-Abelian Schwinger equation

Massless $QCD_2$ is dominated by classical configurations in the large $N_f$ limit. We use this observation to study the theory by finding solutions to equations of motion, which are the non-Abelian generalization of the Schwinger equation. We find that the spectrum consists of massive mesons with $M^2={e^2 N_f\over 2\pi}$ which correspond to Abelian solutions. We generalize previously discovered non-Abelian solutions and discuss their interpretation. We prove a no-go theorem ruling out the existence of soliton solutions. Thus the semi-classical approximation shows no baryons in the case of massless quarks, a result derived before in the strong-coupling limit only.Comment: 17 pages, Latex. 1 figur

The spectrum of states with one current acting on the adjoint vacuum of massless QCD2

We consider a ``one current'' state, which is obtained by the application of a color current on the ``adjoint'' vacuum. This is done in $QCD_2$, with the underlying quarks in the fundamental representation. The quarks are taken to be massless, in which case the theory on the light-front can be ``currentized'', namely, formulated in terms of currents only. The adjoint vacuum is shown to be the application of a current derivative, at zero momentum, on the singlet vacuum. We apply the operator $M^2=2P^+P^-$ on these states and find that in general they are not eigenstates of $M^2$ apart from the large $N_f$ limit. Problems with infra-red regularizations are pointed out. We discuss the fermionic structure of these states.Comment: 18 pages, no figures. v2: minor corrections. v3: added some clarifications and remarks, mainly on the contribution of zero modes. Typos corrected, references added. To appear in Nuclear Physics

Screening in Supersymmetric Gauge Theories in Two Dimensions

We show that the string tension in N=1 two-dimensional super Yang-Mills theory vanishes independently of the representation of the quark anti-quark external source. We argue that this result persists in SQCD_2 and in two-dimensional gauge theories with extended supersymmetry or in chiral invariant models with at least one massless dynamical fermion. We also compute the string tension for the massive Schwinger model, as a demonstration of the method of the calculation.Comment: 8 pages, Latex. Minor changes. Accepted to Phys.Lett.

Subtleties in QCD theory in Two Dimensions

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 $QCD_2$ theory is analyzed in similar terms and peculiar massive states appear, with a mass of $e_c\sqrt {N_F \over 2\pi}$.Comment: 21 page

The String Tension in Two Dimensional Gauge Theories

We review and elaborate on properties of the string tension in two-dimensional gauge theories. The first model we consider is massive QED in the $m\ll e$ limit. We evaluate the leading string tension both in the fermionic and bosonized descriptions. We discuss the next to leading corrections in $m/e$. The next-to-leading terms in the long distance behavior of the quark-antiquark potential, are evaluated in a certain region of external versus dynamical charges. The finite temperature behavior is also determined. In $QCD_2$ we review the results for the string tension of quarks in cases with dynamical quarks in the fundamental, adjoint, symmetric and antisymmetric representations. The screening nature of $SYM_2$ is re-derived.Comment: 25 pages, Latex. v2: several changes, mainly in section

On the stability of quark solitons in QCD

We critically re-examine our earlier derivation of the effective low energy action for QCD in 4 dimensions with chiral fields transforming non-trivially under both color and flavor, using the method of anomaly integration. We find several changes with respect to our previous results, leading to much more compact expressions, and making it easier to compare with results of other approaches to the same problem. With the amended effective action, we find that there are no stable soliton solutions. In the context of the quark soliton program, we interpret this as an indication that the full low-energy effective action must include additional terms, reflecting possible modifications at short distances and/or the non-trivial structure of the gauge fields in the vacuum, such as \neq 0. Such terms are absent in the formalism based on anomaly integration

σ\sigma-models on the quantum group manifolds SLq(2,R)SL_{q}(2,R), SLq(2,R)/Uh(1)SL_{q}(2,R)/U_{h}(1), Cq(2∣0)C_{q}(2|0) and infinitesimal trasformations

The differential and variational calculus on the $SL_{q}(2,R)$ group is constructed. The spontaneous breaking symmetry in the WZNW model with $SL_{q}(2,R)$ quantum group symmetry and in the $\sigma$-models with ${SL_{q}(2,R)/U_{h}(1)}$ ,$C_{q}(2|0)$ quantum group symmetry is considered. The Lagrangian formalism over the quantum group manifolds is discussed. The classical solution of $C_{q}(2|0)$ {$\sigma$}-model is obtained.Comment: LaTex, 7 page