M. N. Chernodub

Abelian dominance and gluon propagators in the maximally Abelian gauge of SU(2) lattice gauge theory

Propagators of the diagonal and the off-diagonal gluons are studied numerically in the maximal Abelian gauge of SU(2) lattice gauge theory. It is found that in the infrared region the propagator of the diagonal gluon is strongly enhanced in comparison with the off-diagonal one. The enhancement factor is about 50 at our smallest momentum 325 MeV. We have also applied various fits to the propagator formfactors.

Anatomy of the lattice magnetic monopoles

We study the Abelian and non-Abelian action densitynear the monopole in the maximal Abelian gauge of SU(2) lattice gauge theory. We find that the non-Abelian action density near the monopoles belonging to the percolating cluster decreases when we approach the monopole center. Our estimate of the monopole radius is R_mon ~ 0.04 fm.Abstract We study the Abelian and non-Abelian action density near the monopole in the maximal Abelian gauge of SU (2) lattice gauge theory. We find that the non-Abelian action density near the monopoles belonging to the percolating cluster decreases when we approach the monopole center. Our estimate of the monopole radius is R mon ≈0.04xa0fm.

Towards Abelian-like formulation of the dual gluodynamics

Abstract We consider gluodynamics in case when both color and magnetic charges are present. We discuss first short distance physics, where only the fundamental |Qm|=1 monopoles introduced via the txa0Hooft 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 |Qm|=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.We consider gluodynamics in case when both color and magnetic charges are present. We discuss first short distance physics, where only the fundamental |Q|=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. We introduce also an effective dual gluodynamics which might be a valid approximation at distances where the monopoles |Q|=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.

Confinement and short distance physics

We consider non-perturbative effects at short distances in theories with confinement. The analysis is straightforward within the Abelian models in which the confinement arises on classical level. In all cases considered (compact U(1) in 3D and 4D, dual Abelian Higgs model) there are non-perturbative contributions associated with short distances which are due to topological defects. In QCD case, both classical and quantum effects determine the role of the topological defects and the theoretical analysis has not been completed so far. Generically, the topological defects would result in 1/Q^2 corrections going beyond the standard Operator Product Expansion. We review existing data on the power corrections and find that the data favor existence of the novel corrections, at least at the mass scale of (1-2) GeV. We indicate crucial experiments which could further clarify the situation on the phenomenological side.Abstract We consider non-perturbative effects at short distances in theories with confinement. The analysis is straightforward within the Abelian models in which the confinement arises on classical level. In all cases considered (compact U (1) in 3 D and 4 D , dual Abelian Higgs model) there are non-perturbative contributions associated with short distances which are due to topological defects. In QCD case, both classical and quantum effects determine the role of the topological defects and the theoretical analysis has not been completed so far. Generically, the topological defects would result in 1/ Q 2 corrections going beyond the standard Operator Product Expansion. We review existing data on the power corrections and find that the data favor existence of the novel corrections, at least at the mass scale of (1–2) GeV. We indicate crucial experiments which could further clarify the situation on the phenomenological side.

Dirac strings and monopoles in the continuum limit of SU(2) lattice gauge theory

Magnetic monopoles are known to emerge as leading non-perturbative fluctuations in the lattice version of non-Abelian gauge theories in some gauges. In terms of the Dirac quantization condition, these monopoles have magnetic charge |Q_M|=2. Also, magnetic monopoles with |Q_M|=1 can be introduced on the lattice via the t Hooft loop operator. We consider the |Q_M|=1,2 monopoles in the continuum limit of the lattice gauge theories. To substitute for the Dirac strings which cost no action on the lattice, we allow for singular gauge potentials which are absent in the standard continuum version. Once the Dirac strings are allowed, it turns possible to find a solution with zero action for a monopole--antimonopole pair. This implies equivalence of the standard and modified continuum versions in perturbation theory. To imitate the nonperturbative vacuum, we introduce then a nonsingular background. The modified continuum version of the gluodynamics allows in this case for monopoles with finite non-vanishing action. Using similar techniques, we construct the t Hooft loop operator in the continuum and predict its behavior at small and large distances both at zero and high temperatures.Magnetic monopoles are known to emerge as leading non-perturbative fluctuations in the lattice version of non-Abelian gauge theories in some gauges. In terms of the Dirac quantization condition, these monopoles have magnetic charge |QM|=2. Also, magnetic monopoles with |QM|=1 can be introduced on the lattice via the t Hooft loop operator. We consider the |QM|=1,2 monopoles in the continuum limit of the lattice gauge theories. To substitute for the Dirac strings which cost no action on the lattice, we allow for singular gauge potentials which are absent in the standard continuum version. Once the Dirac strings are allowed, it turns possible to find a solution with zero action for a monopole–antimonopole pair. This implies equivalence of the standard and modified continuum versions in perturbation theory. To imitate the nonperturbative vacuum, we introduce then a nonsingular background. The modified continuum version of the gluodynamics allows in this case for monopoles with finite non-vanishing action. Using similar techniques, we construct the t Hooft loop operator in the continuum and predict its behavior at small and large distances both at zero and high temperatures.

Towards understanding structure of the monopole clusters

Abstract We consider geometrical characteristics of monopole clusters of the lattice SU (2) gluodynamics. We argue that the polymer approach to the field theory is an adequate means to describe the monopole clusters. Both finite-size and the infinite, or percolating clusters are considered. We find out that the percolation theory allows to reproduce the observed distribution of the finite-size clusters in their length and radius. Geometrical characteristics of the percolating cluster reflect, in turn, the basic properties of the ground state of a system with a gap.

Aharonov-Bohm effect, center monopoles and center vortices in SU(2) lattice gluodynamics

Abstract SU (2) gluodynamics is investigated numerically and analytically in the (Indirect) Maximal Center gauge at finite temperature. The center vortices are shown to be condensed in the confinement phase and dilute in the deconfinement phase. A new physical object, center monopole, is constructed. We show that the center monopole condensate is the order parameter of deconfinement phase transition. The linking of the vortex worldsheets and quark trajectories is identified with the Aharonov-Bohm interaction in an effective Abelian Higgs theory. We conclude that the confinement in the Maximal Center gauge can be explained by a new mechanism called “ the real superconductor mechanism” .

Manifestations of magnetic vortices in the equation of state of a Yang-Mills plasma

The vacuum of Yang-Mills theory contains singular stringlike objects identified with center (magnetic) vortices. Percolation of magnetic vortices is known to be responsible for the color confinement in the low-temperature phase of the theory. In our work, we study properties of the vortices at finite temperature using lattice simulations of

Magnetic monopoles, alive

SU(2)

Monopole order parameter in SU(2) lattice gauge theory

gauge theory. We show that magnetic vortices provide a numerically large contribution to thermodynamic quantities of the gluon plasma in Yang-Mills theory. In particular, we observe that in the deconfinement phase at temperatures