Magnetic Symmetry,Regge Trajectories,and the Linear Confinement in Dual QCD

Using the magnetic symmetry structure of non-Abelian gauge theories, we analyze the flux tube formulation and its implications on the hadronic Regge trajectories and the confinement of color isocharges in magnetically condensed (with as well as without the electric excitations) QCD vacuum. Starting with the fiber bundle structure of QCD, the dual potentials are used to construct the QCD Lagrangian which has been shown to develop a unique flux tube configuration in its dynamically broken phase. The vector mass mode of the condensed vacuum has been shown to play a leading role in flux tube energy and other confinement parameters. Using the flux tube energy and the angular momentum, the Regge trajectories for hadrons have been obtained and the linear confining properties of dual QCD have been established. The dyonic flux tube structure of the condensed QCD vacuum has been obtained by inducing the electric excitation of QCD monopoles and the confining nature along with the linearity of Regge trajectories in dyonically condensed QCD vacuum are shown to remain intact. Implications of the modification in Regge slope parameter, on improving the confining properties of dual QCD vacuum are also discussed. PACS: 12.38.Aw; 11.30.-j; 14.80.Hv; 12.39.Mk An erratum to this article is available at .     

Thermo-field dynamics and quark–hadron phase transition in QCD

Based on the topological structure of gauge theory, an effective dual version of QCD has been reviewed and analyzed for the phase structure and color confining properties of QCD by invoking the dynamical magnetic symmetry breaking. The multi-flux-tube configuration of condensed QCD vacuum has been explored and associated glueball masses and inter-quark potential have been derived. Thermal response of QCD vacuum has been analyzed using path-integral formalism alongwith the mean-field approach and associated thermodynamical potential is used to derive thermal form of glueball masses, monopole condensate, inter-quark potential and monopole density which then lead to an estimate of the critical temperature of QCD phase transition. During its thermal evolution, a smooth transition of hadronic system via a weakly bound QGP phase to the fully deconfined phase is established and the thermal evolution profiles of various parameters are shown to indicate a second-order deconfinement phase transition and the restoration of magnetic symmetry. Monopole density calculations have been shown to lead to gradual evaporation of magnetic condensate into thermal monopoles during QCD phase transition.     

Dual Superconductivity in Abelian Higgs Model of QCD

The study of generalized field associated with Abelian dyons has been undertaken and it has been demonstrated that topologically, a non-Abelian gauge theory is equivalent to a set of Abelian gauge theories supplemented by dyons which undergo condensation leading to confinement and consequently to superconducting model of QCD vacuum, where the Higgs field plays the role of a regulator only. Constructing the effective action for dyonic field in Abelian projection of QCD, it has been demonstrated that any charge (electrical or magnetic) of dyon screens its own direct potential to which it minimally couples and anti-screens the dual potential leading to dual superconductivity in accordance with generalized Meissner effect. In this Abelian projection of QCD an Abelian Higgs model (AHM) has been successfully constructed and it has been shown to incorporate dual superconductivity and confinement as the consequence of dyonic condensation. It has been demonstrated that in AHM t’ Hooft loop creates the string (AHM-string) around which the monopole current under London limit leads to vanishing coherence length in the chromo-magnetic superconductor. It has also been shown that in London limit the squared density of monopole current around AHM-string has a maximum at the distance of the order of penetration length.     

Magnetic symmetry and dyons

A self-consistent theory of dyons in Abelian and non-Abelian limits has been formulated in terms of an extra magnetic symmetry and topological magnetic charge. It has been shown that the restricted gauge potential describes the fields of dyons in terms of two regular (time-like) potentials only when recourse is made to the duality of topological (magnetic) and isocolour (electric) charges. Choosing a suitable Lagrangian density for the system of dyons in non-Abelian gauge theory, the field equations, energy-momentum tensor, Hamiltonian and momentum densities have also been derived and the conservation of the four-linear momentum and the total angular momentum has been demonstrated.     

Gauge Symmetry and Transverse Symmetry Transformations in Gauge Theories

The transverse symmetry transformations associated with the normal symmetry transformations are proposed to build the transverse constraints on the basic vertices in gauge theories. I show that, while the BRST symmetry in non-Abelian gauge theory QCD (Quantum Chromodynamics) leads to the Slavnov-Taylor identity for the quark-gluon vertex which constrains the longitudinal part of thevertex, the transverse symmetry transformation associated with the BRST symmetry enables to derive the transverse Slavnov-Taylor identity for the quark-gluon vertex, which constrains the transverse part of the quark-gluon vertex from the gauge symmetry of QCD.     

Physics on lattice

A short review of physical results obtained recently in lattice gluodynamics and lattice QCD is given. The topics are: formation and breaking of the confining string, spectrum of hadrons, QCD at finite temperature, monopoles and vortices in Abelian and non-Abelian gauge theories.     

Relativistic many-body theory,quantum chromodynamics and neutron stars/supernova

A systematic account of relativistic many-body theory is presented with particular emphasis on the renormalization of finite temperature and density Green's functions and the thermodynamic potential. This is then applied to Quantum Chromodynamics (QCD), the non-Abelian gauge theory of the strong interaction (quarks and gluons), to demonstrate the applicability of perturbation theory of the strong force at high baryon number densities. For an accepted range of the elementary particle parameters, the quark mass and the quark-gluon structure constant, it is shown that QCD determines the major characteristics of heavy mass neutron stars and predicts two supernova mechanisms: hydrodynamic bounce and hyperonization.     

Dielectric function of the QCD vacuum

It is shown that the inverse of the ghost form factor in the Hamilton approach to Yang-Mills theory in Coulomb gauge can be interpreted as the color dielectric function of the QCD vacuum. Furthermore, the horizon condition to the ghost form factor implies that in the infrared the QCD vacuum is a perfect color diaelectric medium and therefore a dual superconductor. The dielectric function is explicitly calculated within a previously developed variational approach, using a specific ansatz for the vacuum wave functional.     

QCD/String holographic mapping and glueball mass spectrum

Recently Polchinski and Strassler reproduced the high energy QCD scaling at fixed angles from a gauge string duality inspired by the AdS/CFT correspondence. In their approach a confining gauge theory is taken as approximately dual to an AdS space with an IR cut-off. Considering such an approximation (AdS slice) we found a one to one holographic mapping between bulk and boundary scalar fields. Associating the bulk fields with dilatons and the boundary fields with glueballs of the confining gauge theory we also found the same high energy QCD scaling. Here, using this holographic mapping, we give a simple estimate for the mass ratios of the glueballs assuming the AdS slice approximation to be valid at low energies. We also compare these results to those coming from supergravity and lattice QCD.Received: 10 September 2003, Revised: 19 November 2003, Published online: 9 January 2004     

Modified Nonlinear Model of Arcsin-Electrodynamics

A new modified model of nonlinear arcsin-electrodynamics with two parameters is proposed and analyzed. We obtain the corrections to the Coulomb law. The effect of vacuum birefringence takes place when the external constant magnetic field is present. We calculate indices of refraction for two perpendicular polarizations of electromagnetic waves and estimate bounds on the parameter γ from the BMV and PVLAS experiments. It is shown that the electric field of a point-like charge is finite at the origin. We calculate the finite static electric energy of point-like particles and demonstrate that the electron mass can have the pure electromagnetic nature. The symmetrical Belinfante energy-momentum tensor and dilatation current are found. We show that the dilatation symmetry and dual symmetry are broken in the model suggested. We have investigated the gauge covariant quantization of the nonlinear electrodynamics fields as well as the gauge fixing approach based on Dirac's brackets.     

Colored magnetic monopoles

We extend Dirac's theory of magnetic monopoles to the case of non-Abelian color gauge groups. Exact classical solution is obtained by making use of the gauge-independent method of Yang-Mills field. The case of broken gauge symmetry is also briefly discussed.     

Finite BRST Mapping in Higher-Derivative Models

We continue the study of finite field-dependent BRST (FFBRST) symmetry in the quantum theory of gauge fields. An expression for the Jacobian of path integral measure is presented, depending on a finite field-dependent parameter, and the FFBRST symmetry is then applied to a number of well-established quantum gauge theories in a form which incudes higher-derivative terms. Specifically, we examine the corresponding versions of the Maxwell theory, non-Abelian vector field theory, and gravitation theory. We present a systematic mapping between different forms of gauge-fixing, including those with higher-derivative terms, for which these theories have better renormalization properties. In doing so, we also provide the independence of the S-matrix from a particular gauge-fixing with higher derivatives. Following this method, a higher-derivative quantum action can be constructed for any gauge theory in the FFBRST framework.     

Parity anomalies in gauge theories in 2 + 1 dimensions

It is shown that the introduction of massless fermions in an abelian gauge theory in 2 + 1 dimensions does not lead to any parity anomaly despite a non-commutativity of limits in the structure function of the odd part of the vacuum polarisation tensor. However, a parity anomaly does exist in non-abelian theories due to a conflict between gauge invariance under large gauge transformations and the parity symmetry.     

Higher gauge theory and a non-Abelian generalization of 2-form electrodynamics

In conventional gauge theory, a charged point particle is described by a representation of the gauge group. If we propagate the particle along some path, the parallel transport of the gauge connection acts on this representation. The Lagrangian density of the gauge field depends on the curvature of the connection which can be calculated from the holonomy around (infinitesimal) loops. For Abelian symmetry groups, say G=U(1), there exists a generalization, known as p-form electrodynamics, in which (p−1)-dimensional charged objects can be propagated along p-surfaces and in which the Lagrangian depends on a generalized curvature associated with (infinitesimal) closed p-surfaces. In this article, we use Lie 2-groups and ideas from higher category theory in order to formulate a discrete gauge theory which generalizes these models at the level p=2 to possibly non-Abelian symmetry groups. An important feature of our model is that it involves both parallel transports along paths and generalized transports along surfaces with a non-trivial interplay of these two types of variables. Our main result is the geometric picture, namely the assignment of non-Abelian quantities to geometrical objects in a coordinate free way. We construct the precise assignment of variables to the curves and surfaces, the generalized local symmetries and gauge invariant actions and we clarify which structures can be non-Abelian and which others are always Abelian. A discrete version of connections on non-Abelian gerbes is a special case of our construction. Even though the motivation sketched so far suggests applications mainly in string theory, the model presented here is also related to spin foam models of quantum gravity and may in addition provide some insight into the role of centre monopoles and vortices in lattice QCD.     

Chiral symmetry breaking at finite temperature in Coulomb gauge QCD

Chiral symmetry breaking at finite temperature is analysed in Coulomb gauge QCD, using a suitably renormalised gap equation. In Coulomb gauge the gap equation is derived using the Ward identities and the Dyson equations for the vector and axial-vector vertices. Making the ladder approximation to the Bethe-Salpeter kernel relates the chiral symmetry breaking parameters to the static quark potential. It is thus possible to use a confining potential in the analysis of chiral symmetry breaking. We extend this to finite temperature. For a confining potential there is no chiral symmetry restoration at any finite temperature.     

A General Theory of Non-Abelian Electrodynamics

The general theory of gauge fields is used to develop a theory of electrodynamics in which the fundamental structure is non-Abelian and in which the internal gauge field symmetry is O(3), based on the existence of circular polarization and the third Stokes parameter. The theory is used to provide an explanation for the Sagnac effect with platform at rest and in motion. The Sagnac formula is obtained by considering the platform in motion to be a gauge transformation. The topological phases can be described straightforwardly with non Abelian electrodynamics, which produces a novel magnetic field component for all types of radiation, a component which is proportional to the third Stokes parameter. The theory provides a natural explanation for the inverse Faraday effect without phenomenology.     

The chiral magnetic effect and chiral symmetry breaking in <Emphasis Type="Italic">SU</Emphasis>(3) quenched lattice gauge theory

We study some properties of the non-Abelian vacuum induced by strong external magnetic field. We perform calculations in the quenched SU(3) lattice gauge theory with tadpole-improved Lüscher-Weisz action and chirally invariant lattice Dirac operator. The following results are obtained: The chiral symmetry breaking is enhanced by the magnetic field. The chiral condensate depends on the strength of the applied field as a power function with exponent ν = 1.6 ± 0.2. There is a paramagnetic polarization of the vacuum. The corresponding susceptibility and other magnetic properties are calculated and compared with the theoretical estimations. There are nonzero local fluctuations of the chirality and electromagnetic current, which grow with the magnetic field strength. These fluctuations can be a manifestation of the Chiral Magnetic Effect.     

不可易规范场的对偶荷

本文讨论了不可易SU(2)规范场的各种规范不变物理量——电荷、对偶荷(磁荷)、电磁场以及有质量矢粒子场的表达式与关系,特别是对偶荷(磁荷)与电荷算符同位旋方向的大范围拓扑性质的关系。