Vacuum Energy, EoS, and the Gluon Condensate at Finite Baryon Density in QCD

The Equation of States (EoS) plays the crucial role in all studies of neutron star properties. Still, a microscopical understanding of EoS remains largely an unresolved problem. We use 2-color QCD as a model to study the dependence of vacuum energy (gluon condensate in QCD) as function of chemical potential \mu\ll \Lambda_{QCD} where we find very strong and unexpected dependence on $\mu$. We present the arguments suggesting that similar behavior may occur in 3-color QCD in the color superconducting phases. Such a study may be of importance for analysis of EoS when phenomenologically relevant parameters (within such models as MIT Bag model or NJL model) are fixed at zero density while the region of study lies at much higher densities not available for terrestrial tests.Comment: Talk at " Quark Confinement and the Hadron Spectrum VII", Ponta Delgada, September 2-7, 200

Intrinsic Strange/Charmed Quarks Inside of a Strangeless/Charmless Hadron

We discuss few, apparently different, but actually tightly related problems: a)Strangeness in the nucleon; b) B --> eta' decays; c)Intrinsic charm in the proton spin problem. We argue that all these problems have a common origin and related to the OZI rule violation in 0^{\pm} vacuum channels . It leads to a noticeable role of a nonvalence component with 0^{\pm} quantum numbers in a hadron.}Comment: Talk given at the ``HADRON 97'' BNL, Brookhaven, August 24-28, 1997, To be published in the proceeding

Confinement- Deconfinement Phase Transition and Fractional Instanton Quarks in Dense Matter

We present arguments suggesting that large size overlapping instantons are the driving mechanism of the confinement-deconfinement phase transition at nonzero chemical potential mu. The arguments are based on the picture that instantons at very large chemical potential in the weak coupling regime are localized configurations with finite size \rho\sim\mu^{-1}. At the same time, the same instantons at smaller chemical potential in the strong coupling regime are well represented by the so-called instanton-quarks with fractional topological charge 1/N_c. We estimate the critical chemical potential mu_c(T) where transition between these two regimes takes place. We identify this transition with confinement- deconfinement phase transition. We also argue that the instanton quarks carry magnetic charges. As a consequence of it, there is a relation between our picture and the standard t'Hooft and Mandelstam picture of the confinement. We also comment on possible relations of instanton-quarks with "periodic instantons", " center vortices", and "fractional instantons" in the brane construction. We also argue that the variation of the external parameter mu, which plays the role of the vacuum expectation value of a "Higgs" field at mu >> \Lambda_{QCD}, allows to study the transition from a "Higgs -like" gauge theory (weak coupling regime, mu>> \Lambda_{QCD}) to ordinary QCD (strong coupling regime, mu<< \Lambda_{QCD}). We also comment on some recent lattice results on topological charge density distribution which support our picture.Comment: Invited talk delivered at the Light Cone Workshop, July 7-15, 2005, Cairns, Australi