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

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

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

Optimal eigenvalues estimate for the Dirac operator on domains with boundary

We give a lower bound for the eigenvalues of the Dirac operator on a compact domain of a Riemannian spin manifold under the \MIT bag boundary condition. The limiting case is characterized by the existence of an imaginary Killing spinor.Comment: 10 page

Calculation of the expansion rate of the three-volume measure in high-energy heavy-ion collisions

In ultrarelativistic heavy-ion collisions the local three-volume measure is expanding in the longitudinal and transverse directions. This is similar to the Hubble-expansion of the universe, except that the former is not locally isotropic. As an example the expansion rate is calculated assuming that the energy-momentum tensor in the central region is that of an ideal fluid, undergoing Bjorken flow in longitudinal direction, and with initial conditions as expected for BNL-RHIC energy. While the longitudinal expansion of three-volume is independent of the energy density of the fluid, in case of 3+1 dimensional expansion the form of the hydrodynamical solution (rarefaction wave or deflagration shock) affects the three-volume expansion rate on the hadronization hypersurface. As a consequence the average expansion rate on that surface depends on the transverse size of the system. This may reflect in an impact-parameter dependence of the formation probability of light nuclei and of the freeze-out temperature of the strong interactions in the system.Comment: 10 Pages REVTEX, 4 Figures; Title slightly modified, 2 new figure

Casimir effect in rugby-ball type flux compactifications

As a continuation of the work in \cite{mns}, we discuss the Casimir effect for a massless bulk scalar field in a 4D toy model of a 6D warped flux compactification model,to stabilize the volume modulus. The one-loop effective potential for the volume modulus has a form similar to the Coleman-Weinberg potential. The stability of the volume modulus against quantum corrections is related to an appropriate heat kernel coefficient. However, to make any physical predictions after volume stabilization, knowledge of the derivative of the zeta function, $\zeta'(0)$ (in a conformally related spacetime) is also required. By adding up the exact mass spectrum using zeta function regularization, we present a revised analysis of the effective potential. Finally, we discuss some physical implications, especially concerning the degree of the hierarchy between the fundamental energy scales on the branes. For a larger degree of warping our new results are very similar to the previous ones \cite{mns} and imply a larger hierarchy. In the non-warped (rugby-ball) limit the ratio tends to converge to the same value, independently of the bulk dilaton coupling.Comment: 13 pages, 6 figures, accepted for publication in PR

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