Yitzhak Frishman

Bosonization and QCD in two dimensions

Abstract Quantum Chromodynamics (QCD) is believed to describe the strong interactions. In the asymptotic domain of large momenta, improved perturbation theory describes phenomena by use of point-like quarks and gluons. But the spectrum and wave functions are in the nonperturbative domain, for which not much can be done analytically in four dimensions. In order to develop analytical methods physicists turned to simpler models, like QCD 2 , the theory in one space and one time dimensions. This review is devoted to the application of bosonization techniques to two-dimensional QCD. We start with a description of the “abelian bosonization”. The methods of the abelian bosonization are applied to several examples like the Thirring model, the Schwinger model and QCD 2 , The failure of this scheme to handle flavored fermions is explained. Wittens non-abelian bosonization rules are summarized including the generalization to the case of fermions with color and flavor degrees of freedom. We discuss in detail the bosonic version of the mass bilinear of colored-flavored fermions in various schemes. The color group is gauged and the full bosonized version of massive multiflavor QCD 2 is written down. The strong coupling limit is taken in the “product scheme” and then in the U ( N F × N C ) scheme. Once the multiflavor QCD 2 action in the interesting region of the low energies is written down, we extract the semiclassical low-lying baryonic spectrum. First, classical soliton solutions the bosonic action are derived. Quantizing the flavor space around those classical solutions produces the masses as well as the flavor properties of the two-dimensional baryons. In addition, low-lying multibaryonic solutions are presented, as well as wave functions and matrix elements of interest, like qq content.

Quark solitons as constituents of hadrons

Abstract We exhibit static solutions of multi-flavour QCD in two dimensions that have the quantum numbers of baryons and mesons, constructed out of quark and anti-quark solitons. In isolation the latter solitons have infinite energy, corresponding to the presence of a string carrying the non-singlet colour flux off to spatial infinity. When Nc solitons of this type are combined, a static, finite-energy, colour singlet solution is formed, corresponding to a baryon. Similarly, static meson solutions are formed out of a soliton and an anti-soliton of different flavours. The stability of the mesons against annihilation is ensured by flavour conservation. The static solutions exist only when the fundamental fields of the bosonized lagrangian belong to U(Nc × Nf) rather than to SU(Nc) × U(Nf). Discussion of flavour-symmetry breaking requires a careful treatment of the normal-ordering ambiguity. Our results can be viewed as a derivation of the constituent quark model in QCD2, allowing a detailed study of constituent mass generation and of the heavy-quark symmetry.

Origins of global anomalies in quantum mechanics

Simple and tractable examples of abelian and non-abelian gauge systems with global anomalies are presented in quantum mechanics. Explicit calculations are done both in the path-integral and hamiltonian formalism. Algebraic criteria are given for the existence of global gauge anomalies. These criteria are applied for every gauge group and many representations. The inconsistency of theories with a global gauge anomaly is discussed.

The spectrum of multiflavor QCD in two dimensions

Abstract A generalization of Wittens non-abelian bosonization to gauge theories can be used to derive an effective action for the strong coupling limit of massive multiflavor QCD in 1 + 1 dimensions. Here we analyze this action and obtain the semi-classical spectrum of soliton solutions corresponding to the two-dimensional baryons. The possible flavor representations of the baryons are found and compared to quark model predictions. We give a formula for the masses of the baryons in terms of their group properties and the quark mass.

Bosonization of colored flavored fermions and QCD in two dimensions

Abstract The WZW action on SU( N C ) × SU( N F ) × U(1) group manifold was proposed as the bosonized theory of free colored and flavored Dirac fermions. Here difficulties are encountered in finding the fermion mass bilinears in terms of boson variables. We thus try an alternative approach using WZW theory on U( N C × N F ) group manifold, where there is no problem with the mass bilinears. After gauging the color we obtain the bosonized form of multiflavor QCD 2 . The strong coupling limit is then taken and the low energy effective action is obtained. We then show that this action, though different from the one we got in the past from the “old” prescription, describes the same low lying semiclassical baryonic spectrum.

Thirring model with U(n) symmetry: Scale invariant only for fixed values of a coupling constant

Generalizations of the Thirring model to Fermi fields with U(n) symmetry are treated. When interactions quadratic in the SU(n) currents are introduced, scale invariance (with anomalous dimensions) is maintained only for values of the coupling gv=0 or gv = 4φ(n+1).

The String Tension in MassiveQCD2

We compute the string tension in massive

Fractional charges: Global and local aspects

{\mathrm{QCD}}_{2}

Gauging of chiral bosonized actions

. 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

Meson-Baryon Scattering in QCD2 for any Coupling

(m\ensuremath{\ll}e)