Finite temperature Euclidean SU (2) lattice gauge fields generated in the confinement phase close to the deconfinement phase transition are subjected to cooling. The aim is to identify long-living, almost-classical local excitations which carry (generically non-integer) topological charge. Two kinds of spatial boundary conditions (fixed holonomy and standard periodic boundary conditions) are applied. For the lowest-action almost-classical configurations we find that their relative probability semi-quantitatively agrees for both types of boundary conditions. We find calorons with unit topological charge as well as (anti-)selfdual lumps (BPS-monopoles or dyons) combined in pairs of non-integer (equal or opposite sign) topological charge. For calorons and separated pairs of equal-sign dyons obtained by cooling we have found that (i) the gluon field is well-described by Kraan-van Baal solutions of the Euclidean Yang-Mills field equations and (ii) the lowest Wilsonfermion modes are well-described by analytic solutions of the corresponding Dirac equation. For metastable configurations found at higher action, the multi-center structure can be interpreted in terms of dyons and antidyons, using the gluonic and fermionic indicators as in the dyon-pair case. Additionally, the Abelian monopole structure and field strength correlators between the centers are useful to analyse the configurations in terms of dyonic constituents. We argue that a semi-classical approximation of the non-zero temperature path integral should be built on superpositions of solutions with non-trivial holonomy.

Results of the study of lattice QCD with two flavors of nonperturbatively improved Wilson fermions at finite temperature are presented. The transition temperature for mπ mρ ∼ 0.8 and lattice spacing a ∼ 0.12 fm is determined. A two-exponent ansatz is successfully applied to describe the heavy quark potential in the confinement phase. * Talk given by V. Bornyakov at "

We discuss some properties of the abelian monopoles in compact U (1) gauge theory and in the SU (2) gluodynamics both on the lattice and in the continuum. §1. IntroductionAbelian monopoles play a key role in the dual superconductor mechanism of confinement 1) in non-abelian gauge theories. Abelian monopoles appear after the so called abelian projection 2) . According to the dual superconductor mechanism a condensation of abelian monopoles should give rise to the formation of an electric flux tube between the test quark and antiquark. Due to a non-zero string tension the quark and the antiquark are confined by a linear potential. This mechanism has been confirmed by many numerical simulations of the lattice gluodynamics 3), 4) which show that the abelian monopoles in the Maximal Abelian projection are responsible for the confinement. The SU (2) string tension is well described by the contribution of the abelian monopole currents 5) ; these currents satisfy the London equation for a superconductor 6), 7) . In Fig. 1, taken from Ref. 7) , the abelian monopole currents near the center of the flux tube formed by the quark-anti-quark pair are shown. It is seen that the monopoles wind around the center of the flux tube just as the Cooper pairs wind around the center of the Abrikosov string. In Fig. 2 taken from Ref. 8) we show the dependence of the value of the monopole condensate Φ inf c on β is shown. It is clearly seen that Φ inf c vanishes at the phase transition and it plays the role of the order parameters 8), 9) . In Ref. 10) the effective lagrangian for monopoles was reconstructed from numerical data for monopole currents for SU (2) gluodynamics in the Maximal Abelian gauge. It occurs that this lagrangian corresponds to the Abelian Higgs model, the monopole are condensed in the classical string tension of the Abrikosov-Nielsen-Olesen string describes well the quantum string tension of the SU (2) gluodynamics. It means that the description of the gluodynamics at large distances in terms of the monopole variables can be very useful.

The bb spectrum is calculated with the use of a relativistic Hamiltonian where the gluon-exchange potential between a quark and an antiquark is taken as in background perturbation theory. We observed that the splittings ∆ 1 = Υ(1D) − χ b (1P) and other splittings between low-lying states are very sensitive to the QCD constant Λ V (n f ) which occurs in the Vector scheme, and good agreement with the experimental data is obtained for Λ V (2-loop, n f = 5) = 325 ± 10 MeV which corresponds to the conventional Λ MS (2−loop, n f = 5) = 238 ± 7 MeV, α s (2−loop, M Z ) = 0.1189 ± 0.0005, and to a large freezing value of the background coupling: α crit (2-loop, q 2 = 0) = α crit (2-loop, r → ∞) = 0.58 ± 0.02. If the asymptotic freedom behavior of the coupling is neglected and an effective freezing coupling α static = const is introduced, as in the Cornell potential, then precise agreement with ∆ 1 (exp) and ∆ 2 (exp) can be reached for the rather large Coulomb constant α static = 0.43 ± 0.02. We predict a value for the mass M (2D) = 10451 ± 2 MeV.

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 ≈ 0.04 f m.

Dipion transitions of the subthreshold bottomonium levels $\Upsilon (nS)\to \Upsilon (n'S) \pi\pi$ with $n>n', n=2,3,4, n'=1,2$ are studied in the framework of the chiral decay Lagrangian, derived earlier. The channels $B\bar B, B\bar B^*+ c.c, B^* \bar B^*$ are considered in the intermediate state and realistic wave functions of $\Upsilon (n S),B$ and $B^*$ are used in the overlap matrix elements. Imposing the Adler zero requirement on the transition matrix element, one obtains 2d and 1d dipion spectra in reasonable agreement with experiment.Comment: 34 pages, 18 figure

We found an additional symmetry hidden in the fermion and Higgs sectors of the Standard Model. It is connected to the centers of the SU(3) and SU(2) subgroups of the gauge group. A lattice regularization of the whole Standard Model is constructed that possesses this symmetry.Comment: 6 pages, no figures. Shortened versio

We study the domain walls connecting different chirally asymmetric vacua in supersymmetric QCD. We show that BPS -saturated solutions exist only in the limited range of mass m ≤ m * ≈ 0.8| < Tr λ 2 > | 1/3 . When m > m * , the domain wall either ceases to be BPS -saturated or disappears altogether. In any case, the properties of the system are qualitatively changed.