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

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 $T\sim T_c$

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

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

Meson masses in large Nf QCD from the Bethe-Salpeter equation

We solve the homogeneous Bethe-Salpeter (HBS) equation for the scalar, pseudoscalar, vector, and axial-vector bound states of quark and anti-quark in large Nf QCD with the improved ladder approximation in the Landau gauge. The quark mass function in the HBS equation is obtained from the Schwinger-Dyson (SD) equation in the same approximation for consistency with the chiral symmetry. Amazingly, due to the fact that the two-loop running coupling of large Nf QCD is explicitly written in terms of an analytic function, large Nf QCD turns out to be the first example in which the SD equation can be solved in the complex plane and hence the HBS equation directly in the time-like region. We find that approaching the chiral phase transition point from the broken phase, the scalar, vector, and axial-vector meson masses vanish to zero with the same scaling behavior, all degenerate with the massless pseudoscalar meson. This may suggest a new type of manifestation of the chiral symmetry restoration in large Nf QCD.Comment: 33 pages, 16 figures. Typos are corrected. Minor corrections and references are added. Version to appear in Phys. Rev.

The Superfluid and Conformal Phase Transitions of Two-Color QCD

The phase structure of two-color QCD is examined as a function of the chemical potential and the number of light quark flavors. We consider effective Lagrangians for two-color QCD containing the Goldstone excitations, spin-one particles and negative intrinsic parity terms. We discuss the possibility of a conformal phase transition and the enhancement of the global symmetries as the number of flavors is increased. The effects of a quark chemical potential on the spin-one particles and on the negative intrinsic parity terms are analyzed. It is shown that the phase diagram that is predicted by the linearly realized effective Lagrangian at tree-level matches exactly that predicted by chiral perturbation theory.Comment: ReVTeX, 23 pages, 3 figures. Discussion of vector condensation extended, two figures added, references adde

Scaling laws near the conformal window of many-flavor QCD

We derive universal scaling laws for physical observables such as the critical temperature, the chiral condensate, and the pion decay constant as a function of the flavor number near the conformal window of many-flavor QCD in the chiral limit. We argue on general grounds that the associated critical exponents are all interrelated and can be determined from the critical exponent of the running gauge coupling at the Caswell-Banks-Zaks infrared fixed point. We illustrate our findings with the aid of nonperturbative functional Renormalization Group (RG) calculations and low-energy QCD models.Comment: 18 pages, 4 figures, references added and discussion expanded (matches JHEP version