QCD with Large Number of Quarks: Effects of the Instanton -- Anti-instanton Pairs

We calculate the contribution of the instanton -- anti-instanton ($I\bar I$) pairs to the vacuum energy of QCD-like theories with $N_f$ light fermions using the saddle point method. We find a qualitative change of the behavior: for $N_f \ge 6$ it starts to oscillate with $N_f$. Similar behaviour was known for quantum mechanical systems interacting with fermions. We discuss the possible consequences of this phenomenon, and its relation to the mechanism of chiral symmetry breaking in these theories. We also discuss the asymptotics of the perturbative series associated with the $I\bar I$ contribution, comparing our results with those in literature.Comment: 11 pages, Late

Pion and Eta Strings

In this paper we construct a string-like classical solution, the pion-string, in the linear sigma model. We then study the stability of the pion-string, and find that it is unstable in the parameter space allowed experimentally. We also speculate on the existance of an unstable eta-string, associated with spontaneous breakdown of the anomalous $U_A(1)$ symmetry in QCD at high temperatures. The implications of the pion and eta strings for cosmology and heavy ion collisions are briefly mentioned.Comment: 5 pages, LATE

Maximum Wavelength of Confined Quarks and Gluons and Properties of Quantum Chromodynamics

Because quarks and gluons are confined within hadrons, they have a maximum wavelength of order the confinement scale. Propagators, normally calculated for free quarks and gluons using Dyson-Schwinger equations, are modified by bound-state effects in close analogy to the calculation of the Lamb shift in atomic physics. Because of confinement, the effective quantum chromodynamic coupling stays finite in the infrared. The quark condensate which arises from spontaneous chiral symmetry breaking in the bound state Dyson-Schwinger equation is the expectation value of the operator $\bar q q$ evaluated in the background of the fields of the other hadronic constituents, in contrast to a true vacuum expectation value. Thus quark and gluon condensates reside within hadrons. The effects of instantons are also modified. We discuss the implications of the maximum quark and gluon wavelength for phenomena such as deep inelastic scattering and annihilation, the decay of heavy quarkonia, jets, and dimensional counting rules for exclusive reactions. We also discuss implications for the zero-temperature phase structure of a vectorial SU($N$) gauge theory with a variable number $N_f$ of massless fermions.Comment: 6 pages, late

Wilsonian Matching of Effective Field Theory with Underlying QCD

We propose a novel way of matching effective field theory with the underlying QCD in the sense of a Wilsonian renormalization group equation (RGE). We derive Wilsonian matching conditions between current correlators obtained by the operator product expansion in QCD and those by the hidden local symmetry (HLS) model. This determines without much ambiguity the bare parameters of the HLS at the cutoff scale in terms of the QCD parameters. Physical quantities for the pi and rho system are calculated by the Wilsonian RGE's from the bare parameters in remarkable agreement with the experiment.Comment: 13 pages, 4 figures, Minor corrections. This is the version to appear in Physical Review

The Instanton Density at Finite Temperatures

For {\it low} T new strict results for the instanton density n(T) are reported. Using the PCAC methods, we express n(T) in terms of {\it vacuum} average values of certain operators, times their {\it calculated} T-dependence. At high T, we discuss the {\it applicability} limits of the perturbative results. We further speculate about possible behaviour of n(T) at $T\sim T_c$

A Mean Field Approach To The Instanton-Induced Effect Close To The QCD Phase Transition

In the instanton models the chiral phase transition is driven by a transition from random instanton-antiinstanton liquid and correlated instanton-antiinstanton molecules. So far this phenomenon was studied by numerical simulations, while we develop alternative semi-analytic approach. For two massless quark flavors, both instantons and ``molecules" generate specific 4-fermion effective interactions. After those are derived, we determine the temperature dependence of the thermodynamic quantities, the quark condensate and the fraction of molecules using standard mean field method. Using Bethe-Salpeter equation, we calculate T-dependence of mesonic correlation functions.Comment: 26 pages, LaTeX, 6 postscript files of 6 figures in additio

Confinement- Deconfinement Phase Transition in Hot and Dense QCD at Large N

We conjecture that the confinement- deconfinement phase transition in QCD at large number of colors N and N_f\ll N at T\neq 0 and \mu\neq 0 is triggered by the drastic change in \theta behavior. The conjecture is motivated by the holographic model of QCD where confinement -deconfinement phase transition indeed happens precisely at the value of temperature T=T_c where \theta dependence experiences a sudden change in behavior[1]. The conjecture is also supported by quantum field theory arguments when the instanton calculations (which trigger the \theta dependence) are under complete theoretical control for T>T_c, suddenly break down immediately below T<T_c with sharp changes in the \theta dependence. Finally, the conjecture is supported by a number of numerical lattice results. We employ this conjecture to study confinement -deconfinement phase transition of dense QCD at large \mu in large N limit by analyzing the \theta dependence. We find that the confinement- deconfinement phase transition at N_f\ll N happens at very large quark chemical potential \mu_c\sim \sqrt{N}\Lambda_{QCD}. This result agrees with recent findings by McLerran and Pisarski[2]. We also speculate on case when N_f\sim N.Comment: 10 pages, final version to appear in Nucl. Phys.

Diquark Bose Condensates in High Density Matter and Instantons

Instantons lead to strong correlations between up and down quarks with spin zero and anti-symmetric color wave functions. In cold and dense matter, $n_b>n_c\simeq 1 fm^{-3}$ and $T<T_c\sim$ 50 MeV, these pairs Bose-condense, replacing the usual $$condensate and restoring chiral symmetry. At high density, the ground state is a color superconductor in which diquarks play the role of Cooper pairs. An interesting toy model is provided by QCD with two colors: it has a particle-anti-particle symmetry which relates$$ and $$ condensates.Comment: 4 pages ReVTeX, 2 eps-figures included using epsf.st

Mean Field, Instantons and Finite Baryon Density

Instantons create a non-local interaction between the quarks, which at finite baryon density leads to the formation of a scalar diquark condensate and color superconductivity. A mean field approach leads to a self-consistent description of the $$and$$ condensates and shows the inevitability of a BCS type instability at the Fermi surface. The role of the rearrangement of the instanton ensemble for the QCD phase transitions is also discussed.Comment: 7 pages LaTeX, 3 eps-figures included, to appear in the Proc. of the 'QCD at Finite Baryon Density'-Workshop (Bielefeld, 27.-30.04.98