The Cheshire Cat Bag Model: Color Anomaly and η′\eta' Properties

We show that color can leak from a QCD bag if we allow for pseudoscalar isoscalar singlet ($\eta'$) coupling at the surface. To enforce total confinement of color an additional boundary term is suggested. New relations between the $\eta'$ mass and decay constant and the QCD gluon condensates are derived and compared with the empirical parameters.Comment: 7 pages, LaTeX, Nordita - 92/68

Instantons in non-Cartesian coordinates

The explicit multi-instanton solutions by 'tHooft and Jackiw, Nohl & Rebbi are generalized to curvilinear coordinates. The idea is that a gauge transformation can notably simplify the expressions obtained after the change of variables. The gauge transform generates a compensating addition to the gauge potential of pseudoparticles. Singularities of the compensating field are irrelevant for physics but may affect gauge dependent quantities.Comment: 10 pages, LaTeX, talk given at Quarks-2000 (Pushkin, Russia) and E.S.Fradkin (Moscow, Russia) conference

Fractal extra dimension in Kaluza-Klein theory

Kaluza-Klein theory in which the geometry of an additional dimension is fractal has been considered. In such a theory the mass of an elementary electric charge appears to be many orders of magnitude smaller than the Planck mass, and the "tower" of masses which correspond to higher integer charges becomes aperiodic.Comment: 3 pages, accepted for publication in Phys.Rev.D (submitted on 3.28.2001

Critical and tricritical exponents of the Gross-Neveu model in the large-NfN_f limit

The critical and the tricritical exponents of the Gross-Neveu model are calculated in the large-$N_f$ limit. Our results indicate that these exponents are given by the mean-field values.Comment: 8 pages, 8 figure

Instantons And Baryon Mass Splittings in the MIT Bag Model

The contribution of instanton-induced effective inter-quark interactions to the baryon mass splittings was considered in the bag model. It is found that results are different from those obtained in the constituent quark model where the instanton effects are like those from one-gluon exchange. This is because in the context of the bag model calculation the one-body instanton-induced interaction has to be included.Comment: 23 pages, report ZTF-93/10 (to appear in Phys.Rev. D

Crystalline ground state in chiral Gross-Neveu and Cooper pair models at finite densities

We study the possibility of spatially non-uniform ground state in (1+1)-dimensional models with quartic fermi interactions at finite fermion densities by introducing chemical potential \mu. We examine the chiral Gross-Neveu model and the Cooper pair model as toy models of the chiral symmetry breaking and the difermion pair condensates which are presumed to exist in QCD. We confirm in the chiral Gross-Neveu model that the ground state has a crystalline structure in which the chiral condensate oscillates in space with wave number 2\mu. Whereas in the Cooper pair model we find that the vacuum structure is spatially uniform. Some discussions are given to explain this difference.Comment: 18 pages, REVTeX, 3 eps figure

A Two-Dimensional Model with Chiral Condensates and Cooper Pairs Having QCD-like Phase Structure

We describe how a generalization of the original Gross-Neveu model from U(N) to O(N) flavor symmetry leads to the appearance of a pairing condensate at high density, in agreement with the conjectured phenomenon of color superconductivity in $(3+1)$-dimensional QCD. Moreover, the model displays a rich phase structure which closely resembles the one expected in two-flavor QCD.Comment: 11 pages, 1 fugure, Presented at TMU-Yale Symposium on Dynamics of Gauge Fields: An External Activity of APCTP, Tokyo, Japan, 13-15 Dec 199