On the infrared behavior of the gluon propagator

Within the framework of gluodynamics, the well-known truncated Schwinger-Dyson equation for the gluon propagator is considered. The general case of power infrared behavior with noninteger exponents is investigated. The technique of extracting nonleading terms of the nonlinear integral equation, defined only by the infrared behavior of the propagator, is developed. The characteristic equation for the exponent is obtained and the interval of its values –1 c 3 is studied. It is shown that the equation for the gluon propagator in question has no solutions for the noninteger and nonhalf-integer power infrared behavior.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 106, No. 2, pp. 250–263, February, 1996.     

Quark and gluon condensates in nuclear matter with Brown-Rho scaling

Quark and gluon condensates in nuclear matter are investigated in a density-dependent relativistic mean-field theory. The in-medium quark condensate decreases rapidly as the density of nuclear matter increases, if the Brown-Rho scaling is included. The decrease in the in-medium quark condensate with the nuclear matter density is consistent with the result predicted by the partial chiral symmetry restoration. The gluon condensate and the influence of the strange quark contents on the gluon condensate in nuclear matter are discussed.     

Double-logarithmic asymptotics of scattering amplitudes in gravity and supergravity

We review the Balitsky-Fadin-Kuraev-Lipatov approach to high-energy scattering in QCD and supersymmetric gauge theories. At a large number of colors, the equations for the gluon composite states in the t-channel have remarkable mathematical properties including their Möbius invariance, holomorphic separability, duality symmetry, and integrability. We formulate a theory of Reggeized gluon interactions in the form of a gauge-invariant effective action local in particle rapidities. In the maximally extended N=4 supersymmetry, the Pomeron is dual to the Reggeized graviton in the ten-dimensional anti-de Sitter space. As a result, the Gribov Pomeron calculus should be reformulated here as a generally covariant effective field theory for the Reggeized gravitons. We construct the corresponding effective action, which allows calculating the graviton Regge trajectory and its couplings. We sum the double-logarithmic contributions for amplitudes with graviton quantum numbers in the t-channel in the Einstein-Hilbert gravity and its supersymmetric generalizations. As the supergravity rank N increases, the double-logarithmic amplitudes begin to decrease rapidly compared with their Born contributions.     

Effective fermion models near a tricritical point

We consider the class of fermion models with a momentum cutoff Λ and an interaction containing derivatives. For the quasilocal fermion model with two coupling constants near a tricritical point, we classify the solutions of mass-gap equations for different values of coupling constants. The mass spectrum of the scalar excitations in the vicinity of the tricritical point is derived and it is found that two scalar exitations always arise when at least one of the constants exceeds its critical value. The mass formation for scalar bound states induced by static gluon fields (gluon condensates) is investigated. Bibliography 5 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 209, 1994, pp. 5–19. Translated by V. A. Andrianov.     

Chirality-violating condensates in QCD and their connection with zero-mode solutions of quark dirac equations

We demonstrate that chirality-violating condensates in massless QCD arise entirely from zero-mode solutions of the Dirac equation in arbitrary gluon fields. We propose a model in which the zero-mode solutions are the ones for quarks moving in the instanton field and calculate the quark condensate magnetic susceptibilities χ of dimension three and κ and ξ of dimension five based on this model. The good correspondence of the values of χ, κ, and ξ obtained using this approach with the values found from the hadronic spectrum is a serious argument that instantons are the only source of chirality-violating condensates in QCD. We discuss the temperature dependence of the quark condensate and show that the phase transition corresponding to the temperature dependence α(T) of the quark condensate as an order parameter is a crossover-type transition.     

Analytic Invariant Charge in QCD with Suppression of Nonperturbative Contributions at Large <Emphasis Type="Italic">Q</Emphasis><Superscript>2</Superscript>

Based on the analytic invariant charge obtained from the results of the standard perturbation theory up to the four-loop approximation, we construct a “synthetic” model of the invariant charge in quantum chromodynamics. In the suggested model, the perturbative discontinuity on the timelike semiaxis in the complex Q² plane is preserved, and nonperturbative contributions not only cancel nonphysical perturbation theory singularities in the infrared region but also rapidly decrease in the ultraviolet region. On one hand, the effective coupling function in this model is enhanced at zero (the dual superconductivity property of the quantum chromodynamics vacuum); on the other hand, a dynamical gluon mass appears. In our approach, fixing the parameter corresponding to the string tension parameter and normalizing (for example, at the point M_τ) entirely fix the synthetic invariant-charge model. The dynamical gluon mass m_g is then fixed and is stable as the number of loops of the original perturbative approximation increases. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 2, pp. 221–239, November, 2005.     

Singular power-law infrared asymptotic behavior of the gluon propagator in the covariant gauge

The complete set of Dyson-Schwinger equations for the propagators of the gluon and Faddeev-Popov ghosts in the Landau gauge is considered. A consistent ansatz for realization of a singularp ^–4 infrared behavior is constructed.State University, Tbilisi. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 102, No. 1, pp. 47–55, January, 1995.     

Holographic Renormalization Group Flow in Anisotropic Matter

Theoretical and Mathematical Physics - We consider holographic renormalization group flow equations in an anisotropic quark—gluon plasma and present anisotropic solutions for some special cases.     

Qcd-parameterization of quark and gluon distributions in the nucleon. The case of “hard” gluons

A new parameterization of quark and gluon distributions in the nucleon is suggested. In contrast to known parameterizations, it is compatible with the predictions of asymptotic-free theories and is, therefore, suitable for carrying out a comparison between QCD and experimental data. The case of “hard” gluons is investigated. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 111, No. 1, pp. 63–76, April, 1997.     

Nontransversality of the gluon polarization tensor in a chromomagnetic background field

We investigate the problem of the transversality of the gluon polarization tensor in a homogeneous Abelian chromomagnetic background field. Using the Slavnov-Taylor identities, we rederive the nontransversality known from a one-loop calculation in the Feynman gauge. In addition, we generalize the whole procedure to an arbitrary gauge-fixing parameter ξ and calculate the ξ-dependent part of the polarization tensor. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 1, pp. 42–56, July, 2006.     

The puzzling infrared of QCD: The landau gauge case

In this contribution we present a short overview of the status of non-perturbative investigations of Landau gauge gluon and ghost propagators in Yang-Mills theories with special emphasis on lattice computations in the infrared region.     

Strongly Intensive Variables and Long-Range Correlations in the Model With a Lattice in the Transverse Plane

Theoretical and Mathematical Physics - In the framework of the quark–gluon string fusion model on the transverse lattice, we study a strongly intensive variable characterizing correlations...     

Three-dimensional Gross-Neveu model in external chromomagnetic fields at finite temperature

A (2+1)-dimensional four-fermion theory at finite temperature in external chromomagnetic fields that model a vacuum gluon condensate is considered. The critical properties of the theory are investigated, and the dependence of the fermion mass on the external field is also found.Institute of High Energy Physics. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 101, No. 3, pp. 391–401, December, 1994.     

One-loop effective action for the gauge field in curved space-time

We consider the one-loop contribution of gluon fluctuations to the gauge-field effective action in a constant homogenous Abelian-like external (background) field in a space with nonzero curvature. We calculate the real and imaginary parts of the effective action and show that the chromomagnetic vacuum remains unstable in spite of the finite curvature of the space. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 117, No. 1, pp. 123–129, October, 1998.     

Stability of models with four-fermion interaction in the presence of vector fields

On the basis of an effective potential for quarks and gluons, for models with fourfermion interaction, stability is examined both with and without vector fields (gluons). The stability conditions relate the main characteristics of four-quark models with quark and gluon condensates.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 189, pp. 3–9, 1991.     

Yang—mills fields with external current

A procedure for quantizing a non-Abelian gauge theory with Lagrangian $$L = - \frac{1}{4}F_{\mu v}^a F_a^{\mu v} + J_a^\mu V_\mu ^a$$ near a nontrivial classical solution is considered. The theories are classified with respect to the external current. The gluon propagator in a model spherically symmetric non-Abelian field is constructed and investigated.     

A relativistic quark model of mesons

We propose a relativistic quantum model to describe mesons comprising a quark and an antiquark with arbitrary masses. The Dirac equations describe the quarks, and the rigid string approximation accounts for the gluon field contribution. The model fits the meson spectra well and determines the masses of the s-, c-, and b-quarks and the relativistic wave functions of compound mesons. Translated from Teoreticheskaya i Mathematicheskaya Fizika, Vol. 116, No. 2, pp. 225–247, August, 1998.     

Quark propagator and spontaneous breaking of chiral symmetry in axial Gauge

An effective nonperturbative model of QCD in the axial gauge based on singular behavior of the gluon propagator of the type 1/k ⁴ is studied. An approximate solution for the quark propagator corresponding to spontaneous breaking of the chiral symmetry is found. The chiral quark condensate is calculated by means of the obtained solutions.Institute of High Energy Physics, Serpukhov. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 90, No. 1, pp. 65–74, January, 1992.