Gluon field strength correlation functions within a constrained instanton model

We suggest a constrained instanton (CI) solution in the physical QCD vacuum which is described by large-scale vacuum field fluctuations. This solution decays exponentially at large distances. It is stable only if the interaction of the instanton with the background vacuum field is small and additional constraints are introduced. The CI solution is explicitly constructed in the ansatz form, and the two-point vacuum correlator of the gluon field strengths is calculated in the framework of the effective instanton vacuum model. At small distances the results are qualitatively similar to the single instanton case; in particular, the invariant structure is small, which is in agreement with the lattice calculations. Received: 18 June 1999 / Revised version: 21 July 1999 / Published online: 17 February 2000     

Instantons in the nonperturbative QCD vacuum

The effect of nonperturbative fields on instantons in QCD is investigated. The nonperturbative vacuum is described in terms of nonlocal gauge-invariant vacuum expectation values of gluon fields. An effective action for instantons is obtained in the bilocal approximation, and it is shown that a stochastic background gluon field leads to an infrared stabilization of instantons. The dependence of a characteristic instanton size on the magnitude of the gluon condensate and on the correlation length in the nonperturbative vacuum is found. The size distribution of instantons that is obtained here is compared with the results of lattice calculations.     

$VA\widetilde{V}$ correlator within the instanton vacuum model

The correlator of vector and non-singlet axial-vector currents in the external electromagnetic field is calculated within the instanton liquid model of the QCD vacuum. In general the correlator has two Lorentz structures: longitudinal, w_L, and transversal, w_T, with respect to the axial-vector index. Within the instanton model the saturation of the anomalous w_L structure is demonstrated. It is known that in the chiral limit the transversal structure w_T is free from perturbative corrections. In this limit within the instanton model we calculate the transversal invariant function w_T at arbitrary space-like momentum transfer q and show the absence of power corrections to this structure at large q². Instead there arise exponential corrections to w_T at large q² reflecting non-local properties of the QCD vacuum. The slope of w_T at zero virtuality, the QCD vacuum magnetic susceptibility of the quark condensate and its momentum dependence are estimated.Received: 7 May 2005, Published online: 6 July 2005     

False vacuum decay in a brane world cosmological model

The false vacuum decay in a brane world model is studied in this work. We investigate the vacuum decay via the Coleman-de Luccia instanton, derive explicit approximative expressions for the Coleman-de Luccia instanton which is close to a Hawking-Moss instanton and compare the results with those already obtained within Einstein's theory of relativity.     

Instantons and meson correlation functions in QCD

Various QCD correlators are calculated in the instanton liquid model in zeromode approximation and 1/N _c expansion. Previous works are extended by including dynamical quark loops. In contrast to the original “perturbative” 1/N _c approximation, not all quark loops are suppressed. Renormalization of the instanton density allows the identification of the density with the gluon condensate even in presence of dynamical quark loops. In the flavor singlet meson correlators a chain of quark bubbles survives the N _c → ∞ limit causing a massive η′ in the pseudoscalar correlator while keeping massless pions in the triplet correlator. The correlators are plotted and meson masses and couplings are obtained from a spectral fit. They are compared to the values obtained from numerical studies of the instanton liquid and to experimental results.     

Singlet $$\tilde V$$ correlator within the instanton vacuum model

The correlator of singlet axial-vector and vector currents in the external electromagnetic field is studied within the instanton liquid model of the QCD vacuum. In the chiral limit, we calculate the longitudinal w _L ⁽⁰⁾ and transversal w _T ⁽⁰⁾ , with respect to the axial-vector index, invariant amplitudes at an arbitrary spacelike momentum transfer q. It is demonstrated how the anomalous longitudinal part of the correlator is renormalized at low momenta due to the presence of the U _A (1) anomaly.     

Spin effects in instanton models

Nonperturbative nolocal structure of QCD vacuum is well described by instanton model. Specific helicity and flavor structure of zero modes of quarks, in instanton field allows simultaneously to explain some important features of low-and high-energy hadron phenomemology. The basic characteristics of hadron spectrum, partonic sum rules, heavyquark potential etc within the instanton liquid model are briefly discussed.     

Off-diagonal quark distributions in pions in the effective single-instanton approximation

Nonperturbative functions that parametrize off-diagonal hadronic matrix elements of the light-cone leading-twist quark operators are considered. These functions are calculated within the proposed relativistic quark model allowing for the nontrivial structure of the QCD vacuum, special attention being given to gauge invariance. Hadrons are treated as bound states of quarks; strong-interaction quark-pion vertices are described by effective interaction Lagrangians generated by instantons. The parameters of the instanton vacuum, such as the effective radius of the instanton and the quark mass, are related to the vacuum expectation values of the quark-gluon operators of the lowest dimension and to low-energy pion observables.     

Nonperturbative contribution to the quark form factor within the instanton model

The nonperturbative effects in the quark form factor are considered in the Wilson loop formalism, within the framework of the instanton liquid model. For the integration path corresponding to this form factor, the explicit expression for the vacuum expectation value of the Wilson operator is found to the leading order. It is shown that the instantons produce the power-like corrections to the perturbative result, which are comparable in magnitude with the perturbative part at the scale of order of the inverse average instanton size. It is demonstrated that the instanton contributions to the quark form factor are exponentiated to high orders in the small instanton density parameter.Received: 30 September 2002, Published online: 22 October 2003PACS: 12.38.-t Quantum chromodynamics - 11.15.Tk Other nonperturbative techniques     

Scaling and enhanced symmetry at the quantum critical point of the sub-ohmic Bose-Fermi Kondo model

We consider the finite-temperature scaling properties of a Kondo-destroying quantum critical point in the Ising-anisotropic Bose-Fermi Kondo model (BFKM). A cluster-updating Monte Carlo approach is used, in order to reliably access a wide temperature range. The scaling function for the two-point spin correlator is found to have the form dictated by a boundary conformal field theory, even though the underlying Hamiltonian lacks conformal invariance. Similar conclusions are reached for all multipoint correlators of the spin-isotropic BFKM in a dynamical large-N limit. Our results suggest that the quantum critical local properties of the sub-Ohmic BFKM are those of an underlying boundary conformal field theory.     

On the possibility of the dual Meissner effect induced by instantons

The classical Yang-Mills equation of motion is numerically investigated in the Lorentz gauge for a SU(2) gauge group. The color-electric field of two point-like charges is studied in the “empty” vacuum and in a state with an instanton present. The major effect for a fixed orientation of the instanton is that the color-electric field lines are expelled or attracted from the instanton region depending on the orientation of the instanton. If over the orientations of the instanton is averaged, this effect drops out. In this case of a random instanton orientation, we find that the external color-electric field is expelled from the instanton core. The origin of this effect is discussed. Received: 5 September 1997 / Published online: 23 February 1998     

Properties of lightest mesons at finite temperature and quark/baryon chemical potential in the instanton model of the QCD vacuum

The paper is focused on calculating the finite temperature and quark/baryon chemical potential dependencies of the quark condensate and the π-and σ-meson masses in the subcritical region in the instanton model of the QCD vacuum. The impact of phononlike excitation of instanton liquid on the characteristics of the σ meson in such an environment is also examined.     

Instantons and vacuum expectation values in the Schwinger model

Vacuum expectation values for the Schwinger model are computed within the path integral formalism for an instanton vacuum. The calculations are done in flat Euclidean space and use the wellknown anomaly result. It can be demonstrated that the instanton vacuum is absolutely necessary to obtain a consistent quantization. At last the results are compared to a similar treatment on the sphere and to the operator solution of the Schwinger model.Supported by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Projekt Nr. P8444-TEC     

Pion-distribution amplitude within the instanton model

The leading-twist pion-distribution amplitude is obtained at a low normalization scale of order ρ _c (inverse average size of an instanton). Pion dynamics, consistent with gauge invariance and low-energy theorems, is considered within the instanton vacuum model. The results are QCD-evolved to higher momentum-transfer values and are in agreement with recent data from CLEO on the pion transition form factor. It is also shown that some previous calculations violate the axial Ward-Takahashi identity.     

Finite temperature vacuum excitations for a field theory with dynamical symmetry breaking

The renormalized finite-temperature σ-propagator for the Gross-Neveu model is constructed in the large -N limit. The singularity structure of this Green function is used to analyze the finite-temperature vacuum excitations. It is shown that, at a finite temperature below the critical one, a fermion-antifermion bound state is formed with a non-vanishing binding energy in contrast to the zero-temperature case, where the binding energy is known to vanish.     

Study of Vacuum Structure by Low-Lying Eigenmodes of Overlap-Dirac Operator

APE smearing and overlap-Dirac operator are combined to filter vacuum configurations. The structures of vacuum are studied by low-lying eigenmodes of the overlap-Dirac operator, which exhibits that instanton liquid model can be used.     

Instanton induced chiral symmetry breaking in extended QCD model

A mechanism for instanton induced chiral symmetry breaking in an extended QCD model (QCD with fundamental scalars) is proposed to describe quarks and gluons inside a baryon. The model Lagrangian that we use has the same symmetry properties as QCD. The scalar fields are shown to develop vacuum expectation values in the instanton background and generate masses for the three generation of quarks. The minimization condition is also used to break the flavour symmetry to make the -quark heavier that the and quarks. Received: 16 August 1996 / Revised version: 15 October 1997 / Published online: 26 February 1998     

Information on the QCD phase transition and the vacuum permeability from the interquark potential

A method for the calculation of the interquark potential resulting from the instanton induced phase transition in the QCD vacuum is described and it is shown that good agreement is obtained with successful phenomenological potentials for parameter values close to those expected from naive instanton calculations.