Effective monopole potential for SU(2) lattice gluodynamics in the spatial maximal Abelian gauge

We investigate the dual superconductor hypothesis in finite-temperature SU(2) lattice gluodynamics in the spatial maximal Abelian gauge. This gauge is more physical than the ordinary maximal Abelian gauge due to absence of nonlocalities in the temporal direction. We show numerically that in the spatial maximal Abelian gauge the probability distribution of the Abelian monopole field is consistent with the dual superconductor mechanism of confinement: the Abelian condensate vanishes in the deconfinement phase and is nonzero in the confinement phase. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 3, 166–170 (10 February 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Anatomy of isolated monopole in Abelian projection of SU(2) lattice gauge theory

We study the structure of isolated static monopoles in the maximal Abelian projection of SU(2) lattice gluodynamics. Our estimation of the monopole radius is: R ^mon≈0.06 fm.     

On a projection in dependence on monopole condensate in the lattice SU(2) gauge theory

We study the temperature dependence of the monopole condensate in different Abelian projections of the SU(2) lattice gauge theory in the thermodynamic limit. Using the Fröhlich-Marchetti monopole creation operator, we show numerically that the monopole condensate depends strongly on the choice of the Abelian projection. Contrary to the claims in the literature, we observe that, in the Abelian-Polyakov gauge and in the field strength gauge, the monopole condensate does not vanish at the critical temperature in the large-volume limit. Therefore, the monopole condensate in these gauges is not an order parameter of the confinement-deconfinement phase transition.     

Towards Abelian-like formulation of the dual gluodynamics

We consider gluodynamics in case when both color and magnetic charges are present. We discuss first short distance physics, where only the fundamental |Q_m|=1 monopoles introduced via the 't Hooft loop can be considered consistently. We show that at short distances the external monopoles interact as pure Abelian objects. This result can be reproduced by a Zwanziger-type Lagrangian with an Abelian dual gluon and ordinary gluons in an adjoint representation. We introduce also an effective dual gluodynamics which might be a valid approximation at distances where the monopoles |Q_m|=2 can be considered as point-like as well. Assuming the monopole condensation we arrive at a model which is reminiscent in some respect of the Abelian Higgs model but, unlike the latter leaves space for the Casimir scaling.     

On projection (in)dependence of the dual superconductor mechanism of confinement

We study the temperature dependence of the monopole condensate in different Abelian projections of the SU(2) gauge theory on the lattice. Using the Fröhlich-Marchetti monopole creation operator, we show numerically that the monopole condensate depends on the choice of the Abelian projection.     

Monopole creation operator in the presence of matter

The monopole creation operator proposed recently by Fröhlich and Marchetti is investigated in the Abelian Higgs model with compact gauge field. We show numerically that the creation operator detects the condensation of monopoles in the presence of the dynamical matter field.     

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.     

Creating a monopole in 4D gauge theories

The problem of defining the second quantized monopole creation operator in non-Abelian gauge theories is discussed and exemplified by the (3 + 1)-dimensional Georgi-Glashow model. We construct the “coherent state” operator M(x) that creates the Coulomb magnetic field in terms of the Dirac singular electromagnetic potential. Our calculation of the vacuum expectation value of this operator 〈M(x)〉 in the confining phase indicates that it is free from the singularity along the Dirac string and in the leading order of perturbation theory the 〈M(x)〉 vanishes as a power of the volume of the system. This supports the conception that inclusion of the nonperturbative effects introduces an effective infrared cutoff on the calculation providing the finiteness of vacuum expectation value 〈M(x)〉. The text was submitted by the authors in English.     

String representation of SU(3) gluodynamics in the Abelian projection

A dual Ginzburg-Landau model corresponding to SU(3) gluodynamics in the Abelian projection is studied. A string theory describing QCD string dynamics is obtained in this model. The interaction of static quarks in mesons and baryons is investigated in an approximation to leading order. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 2, 109–114 (25 July 1998)     

Exact Solutions of a Quark Plasma Equilibrium in the Abelian Dominance Approximation

Abstract

Stationary kinetic equations for a quark plasma (QP) in the Abelian dominance approximation are reduced to the nonlinear system of A ₂-periodic Toda chains (with elliptic operator). Using solutions of this system, which are found with the help of the first integrals and Hirota’s method, such characteristics of QPas the distribution function and the potential of the self-consistent field are constructed.     

Monopoles in gluodynamics and blocking from continuum to lattice

We review the method of blocking of topological defects from continuum to lattice as a nonperturbative tool to construct effective actions for these defects. The actions are formulated in the continuum limit, while the couplings of these actions can be derived from simple observables calculated numerically on lattices with a finite lattice spacing. We demonstrate the success of the method in deriving the effective actions for Abelian monopoles in the pure SU(2) gauge models in an Abelian gauge. In particular, we discuss the gluodynamics in three and four spacetime dimensions at zero and nonzero temperatures. Besides the action, the quantities of our interest are the monopole density, the magnetic Debye mass, and the monopole condensate.     

Gravity of monopole and string and the gravitational constant in 3He-A

We discuss the effective metric produced in superfluid ³He-A by such topological objects as the radial disgyration and monopole. In relativistic theories these metrics are similar to that of the local string and global monopole, respectively. But in ³He-A they have a negative angle deficit, which corresponds to a negative mass of the topological objects. The effective gravitational constant in superfluid ³He-A, deduced from a comparison with relativistic theories, is G∼Δ⁻², where the gap amplitude Δ plays the part of the Planck energy. G depends on temperature roughly as (1−T ²/T _c ² )⁻² and corresponds to a screening of Newton’s constant. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 9, 666–671 (10 May 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Wilson area law in a gas of Abelian monopoles

A gas of Abelian monopoles is studied taking account of the interaction of the particles. The Wilson average, for which the law of areas is obtained with allowance for Debye screening, is calculated, with a “tension” coefficient proportional to the monopole density. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 2, 133–138 (25 January 1997)     

Dirac Operators Coupled to the Quantized Radiation Field: Essential Self-adjointness à la Chernoff

We study the Dirac operator D ₀ in an external potential V, coupled to a quantized radiation field with energy H _f and vector potential A. Our result is a Chernoff-type theorem, i.e., we prove, for the operator D ₀+α · A+V +λ H _f with λ ∈{0, 1}, that the essential self-adjointness is not affected by the behavior of V at ∞.      

Abelian dyons in the maximal Abelian projection of SU(2) gluodynamics

Correlations of the topological charge Q, the electric current J ^e, and the magnetic current J ^m in SU(2) lattice gauge theory in the maximal Abelian projection are investigated. It is found that the correlator 〈〈QJ ^eJ^m〉〉 is nonzero for a wide range of values of the bare charge. It is shown that: (i) the Abelian monopoles in the maximal Abelian projection are dyons which carry fluctuating electric charge; (ii) the sign of the electric charge e(x) coincides with that of the product of the monopole charge m(x) and the topological charge density Q(x). Pis’ma Zh. éksp. Teor. Fiz. 69, No. 3, 161–165 (10 February 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Topological field patterns in the Yang-Mills theory

We present a formalism where the topological configurations of pure Yang-Mills theory are characterised using gauge fields alone. Here, we obtain an expression for the charges of these topologicalSO(3) gauge field configurations in terms of the Abelian vector potentials. In this formalism we analyse the ’t Hooft-Polyakov monopole solution.     

Magnetoexcitonic states in a quantum ring with the Winternitz-Smorodinsky confinement potential

We investigate magnetoexcitonic states in the Ga_{1−x 1}Al_{x 1}As/GaAs/Ga_{1−x 2}Al_{x 2} As quantum ring with the Winternitz-Smorodinsky confinement potential. A homogeneous magnetic field is directed perpendicularly to the ring plane. The Coulomb interaction between the electron and hole is assumed as weak and is considered in the framework of perturbation theory. Obtained results show that the more realistic Winternitz-Smorodinsky confinement potential, which takes into account a peculiar smoothing of the confinement potential profile, leads to raising of the electron energy levels as compared to the case of a finite-height rectangular confinement potential.     

Berezinskii-Kosterlitz-Thouless phase transitions in two-dimensional systems with internal symmetries

The Berezinskii-Kosterlitz-Thouless (BKT) phase transitions in two-dimensional systems with internal continuous Abelian symmetries are investigated. In order for phase transitions to occur, the kinetic part of the action of the system must have conformal invariance, and the vacuum manifold must be degenerate and have a discrete Abelian homotopy group π ₁. In this case topological excitations have a logarithmically divergent energy and can be described by effective theories that generalize the two-dimensional Euclidean sine-Gordon theory, which is an effective theory of the original XY model. In particular, the effective actions are found for chiral models on the maximal Abelian tori T _G of the simple compact Lie groups G. The critical properties of the possible effective theories are found, and it is shown that they are characterized by the Coxeter numbers h _G of lattices of the and ℤ series and can be interpreted as properties of conformal theories with an integer central charge C=n, where n is the rank of the groups π ₁ and G. The possibility of reconstructing the complete symmetry of G in the massive phase is also discussed. Zh. éksp. Teor. Fiz. 116, 2045–2057 (December 1999)     

Many-body Hamiltonian with screening parameter and ionization energy

We prove the existence of a Hamiltonian with ionization energy as part of the eigenvalue, which can be used to study strongly correlated matter. This eigenvalue consists of total energy at zero temperature (E ₀) and the ionization energy (ξ). We show that the existence of this total energy eigenvalue, E ₀±ξ, does not violate the Coulombian atomic system. Since there is no equivalent known Hamilton operator that corresponds quantitatively to ξ, we employ the screened Coulomb potential operator (Yukawa-type), which is a function of this ionization energy to analytically calculate the screening parameter (σ) of a neutral helium atom in the ground state. In addition, we also show that the energy level splitting due to spin-orbit coupling is inversely proportional to ξ eigenvalue, which is also important in the field of spintronics.     

Hidden Grassmann Structure in the XXZ Model II: Creation Operators

In this article we unveil a new structure in the space of operators of the XXZ chain. For each α we consider the space of all quasi-local operators, which are products of the disorder field with arbitrary local operators. In analogy with CFT the disorder operator itself is considered as primary field. In our previous paper, we have introduced the annhilation operators b(ζ), c(ζ) which mutually anti-commute and kill the “primary field”. Here we construct the creation counterpart b*(ζ), c*(ζ) and prove the canonical anti-commutation relations with the annihilation operators. We conjecture that the creation operators mutually anti-commute, thereby upgrading the Grassmann structure to the fermionic structure. The bosonic operator t*(ζ) is the generating function of the adjoint action by local integrals of motion, and commutes entirely with the fermionic creation and annihilation operators. Operators b*(ζ), c*(ζ), t*(ζ) create quasi-local operators starting from the primary field. We show that the ground state averages of quasi-local operators created in this way are given by determinants. Membre du CNRS On leave of absence from Skobeltsyn Institute of Nuclear Physics, MSU, 119992 Moscow, Russia Dedicated to the memory of Alexei Zamolodchikov