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.

On the Significance of the Quantity "A Squared"

We consider the gauge potential A and argue that the minimum value of the volume integral of A squared (in Euclidean space) may have physical meaning, particularly in connection with the existence of topological structures. A lattice simulation comparing compact and non-compact ``photodynamics'' shows a jump in this quantity at the phase transition, supporting this idea.Comment: 6 pages, one figur

Embedded Topological Defects in Hot Electroweak Theory: a Lattice Study

We study the properties of Nambu monopoles and Z-vortices in the 3D lattice SU(2) Higgs theory which represents the Standard Model at high temperature. We show that the densities of the Nambu monopoles and the Z-vortices are O(1) in the symmetric phase and generically small in the Higgs phase. Near to the critical Higgs mass and in the vicinity of the phase transition the densities are no more negligible in the broken phase. The percolation probability of the Z-vortex lines is found as a new disorder parameter for this phase transition. We conclude that the transition to the symmetric phase is accompanied by Z-vortex condensation. Simulations comparing elementary and extended vortices and monopoles at different \beta_G values, aiming to show that the density of vortices and monopoles of fixed physical size might have a well-defined continuum limit, gives encouraging but so far inconclusive results.Comment: 13 pages, LaTeX, 8 figures, epsf.sty needed; revision: minor changes and reference adde

Z-Vortex Percolation in the Electroweak Crossover Region

We study the statistical properties of Z-vortices and Nambu monopoles in the 3D SU(2) Higgs model for a Higgs mass M_H \approx 100 GeV near and above the crossover temperature, where these defects are thermally excited. Although there is no phase transition at that strong selfcoupling, we observe that the Z-vortices exhibit the percolation transition that has been found recently to accompany the first order thermal transition that exists at smaller Higgs mass. Above the crossover temperature percolating networks of Z-vortex lines are ubiquitous, whereas vortices form a dilute gas of closed vortex loops and (Nambu) monopolium states on the low-temperature side of the crossover. The percolation temperature turns out to be roughly independent of the lattice spacing. We find that the Higgs modulus is smaller (the gauge action is larger) inside the vortices, compared to the bulk average. This correlation becomes very strong on the low-temperature side. The percolation transition is a prerequisite of some string mediated baryon number generation scenarios.Comment: 16 pages, LaTeX, 12 figures, epsf.sty needed; final version to appear in Phys. Lett.

Interaction of electric charges in (2+1)D magnetic dipole gas

The interaction of electrically charged particles in a dilute gas of point--like magnetic dipoles is studied. We show that the interaction potential at small distances has a linear piece due to overlap of the dipole clouds gathered near electric sources. At large distances the potential becomes of the Coulomb type with non-perturbatively renormalized charge of the test particle. The physical applications of these results are discussed.Comment: 23 pages, 12 EPS figures, RevTeX, uses epsfig.sty; misprints corrected (to appear in Phys.Rev.D

The topological structure of SU(2) gluodynamics at T > 0 : an analysis using the Symanzik action and Neuberger overlap fermions

We study SU(2) gluodynamics at finite temperature on both sides of the deconfining phase transition. We create the lattice ensembles using the tree-level tadpole-improved Symanzik action. The Neuberger overlap Dirac operator is used to determine the following three aspects of vacuum structure: (i) The topological susceptibility is evaluated at various temperatures across the phase transition, (ii) the overlap fermion spectral density is determined and found to depend on the Polyakov loop above the phase transition and (iii) the corresponding localization properties of low-lying eigenmodes are investigated. Finally, we compare with zero temperature results.Comment: 20 pages, 21 figures, one new figure, two overloaded figures split in two, minor clarifying changes throughout the text, final version accepted by Physical Review

Magnetic monopoles, alive

We review recent developments in understanding the physics of the magnetic monopoles in unbroken non-Abelian gauge theories. Since numerical data on the monopoles are accumulated in lattice simulations, the continuum theory is understood as the limiting case of the lattice formulation. In this review, written for a memorial volume dedicated to the memory of Academician A.B. Migdal, we emphasize physical effects related to the monopoles. In particular, we discuss the monopole-antimonopole potential at short and larger distances as well as a dual formulation of the gluodynamics, relevant to the physics of the confinement.Comment: 24+1 pp., Latex2e, no figure