Confining string and its widening in HP1 embedding approach

Structure of confining string in terms of the topological charge density and the action density is studied in SU(2) Yang-Mills theory on the lattice using HP1 sigma-model embedding approach. We find that the confining flux tube noticeably suppresses both the topological charge and the action densities. Beyond the string formation length the string cross section in terms of these quantities is well described by a Gaussian profile. In both cases the squared string width is found to be a logarithmic function of the string length confirming the Luscher widening of the chromoelectric string. Characteristic string scales in terms of the topological and action densities are estimated as well.Comment: 13 pages, 20 figures, RevTeX 4.0; replaced to match published versio

Topological Content of the Electroweak Sphaleron on the Lattice

3D electroweak sphalerons on the lattice are used as test configurations for definitions of various topological defects. In the maximally Abelian gauge they are shown to contain a symmetric array of Abelian monopoles and anti-monopoles connected by two kinds of Abelian vortex strings. Gauge-invariant lattice definitions of the Nambu monopole and the Z-vortex string are formulated which correspond to Abelian projection from the unitary gauge. The sphalerons contain in their core just one (non-Abelian) Nambu monopole-anti-monopole pair (connected by a Z-string) in an unstable saddle point bound state. This provides an example for the monopole-pair unbinding mechanism expected to work at the electroweak phase transition. The definitions of defects developed here will be used in future studies of topological aspects of this transition.Comment: 13 pages, LaTeX, 9 figures, uses epsf.sty; The sign in eq.(13) is corrected; to appear in Phys.Lett.

Monopoles and Confining Strings in QCD

We review the recent results in the physics of the magnetic monopoles in gluodynamics and a dual formulation of non-Abelian theories, relevant to the physics of the confinement. It occurs that the dual gluon is a U(1) gauge boson, despite of the fact that usual gluons are non-Abelian. The effective infrared Lagrangian for gluodynamics is suggested which leads to the Casimir scaling of the string tension for quarks in various representations. We also show that the results of the calculations in lattice gauge theories confirm our theoretical predictions.Comment: 36 pp., Latex2e, 9 figures (epsfig). Review based on the plenary talks of M.I.Polikarpov at International Conference "Supersymmetry and Quantum Field Theory", dedicated to the 75th birthday anniversary of Dmitrij Volkov (NSC KIPT, Kharkov, Ukraine 25 - 29 July, 2000) and XVIII CFIF Autumn School "Topology of strongly correlated systems" (Lisbon 8-13 October 2000

Mass Gap, Abelian Dominance and Vortex Dynamics in SU(2) Spin Model

We discuss a new approach to the investigation of the nature of the mass gap in spin systems with continuous global symmetries which is much analogous to the method of abelian projection in the gauge theories. We suggest that the abelian degrees of freedom, in particular, abelian vortices are responsible for the mass gap generation phenomena in the non-abelian spin systems. To check our hypothesis we study numerically the three-dimensional SU(2) spin model in the Maximal Abelian projection. We find that the abelian mass gap in the projected theory coincides with the full non-abelian mass gap within numerical errors. The study of the percolation properties of the abelian vortex trajectories shows that the phase transition and the mass gap generation in the 3D SU(2) spin model are driven by the abelian vortex condensation.Comment: 12 pages, LaTeX, 4 figures, uses epsf.sty; Fig.3 is replaced and a few comments are adde