On the non-Abelian Stokes theorem in SU(2) gluodynamics

We discuss the non-Abelian Stokes theorem for SU(2) gauge fields which avoids both additional integration variables and surface ordering. The idea is to introduce the instant color orientation of the flux piercing the loop. The non-Abelian Stokes theorem is also considered on the lattice and various terms contributing to the trace of the Wilson loop are discussed.Comment: 3 pages, 2 figures, Lattice2003(topology

On Nonexistence of Magnetic Charge in Pure Yang-Mills Theories

We prove that magnetic charge does not exist as a physical observable on the physical Hilbert space of the pure SU(2) gauge theory. The abelian magnetic monopoles seen in lattice simulations are then interpreted as artifacts of gauge fixing. The apparent physical scaling properties of the monopole density in the continuum limit observed on the lattice are attributed to the correct scaling properties of physical objects - magnetic vortices, as first argued by Greensite et. al. We can show that a local gauge transformation of a certain type can " create" abelian monopole-antimonopole pairs along magnetic vortices. This gauge transformation exists in pure SU(N) gauge theory at any $N$.Comment: Some references and comments adde

On the Emerging Phenomenology of <(A_\mu)^2>

We discuss phenomenology of the vacuum condensate in pure gauge theories, where A_\mu is the gauge potential. Both Abelian and non-Abelian cases are considered. In case of the compact U(1) the non-perturbative part of the condensate is saturated by monopoles. In the non-Abelian case, a two-component picture for the condensate is presented according to which finite values of order \Lambda_{QCD}^2 are associated both with large and short distances. We obtain a lower bound on the by considering its change at the phase transition. Numerically, it produces an estimate similar to other measurements. Possible physical manifestations of the condensate are discussed.Comment: 17 pp., Latex2e, 3 figure

Aharonov--Bohm Effect in 3D Abelian Higgs Theory

We study a field--theoretical analogue of the Aharonov--Bohm effect in the 3D Abelian Higgs Model: the corresponding topological interaction is proportional to the linking number of the vortex and the particle world trajectories. We show that the Aharonov--Bohm effect gives rise to a nontrivial interaction of tested charged particles.Comment: LaTeX, 3 pages, 1 figure, uses epsf.sty; talk presented at LATTICE96(topology), St. Louis, US

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.Comment: 11 pp., Latex2e, 4 figures, epsfig.sty. Accepted for publication in Physics Letters

Self-tuning of the P-vortices

We observe that on the currently available lattices the non-Abelian action associated with the P-vortices is ultraviolet divergent. On the other hand, the total area of the vortices scales in physical units. Since both the ultraviolet and infrared scales are manifested and there is no parameter to tune, the observed phenomenon can be called self tuning.Comment: Lattice2003(topology

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.

Heavy monopole potential in gluodynamics

We discuss predictions for the interaction energy of the fundamental monopoles in gluodynamics introduced via the 't Hooft loop. At short distances, the heavy monopole potential is calculable from first principles. At larger distances, we apply the Abelian dominance models. We discuss the measurements which would be crucial to distinguish between various models. Non-zero temperatures are also considered. Our predictions are in qualitative agreement with the existing lattice data. We discuss further measurements which would be crucial to check the model.Comment: 3 pages, 1 figure, Lattice2001(confinement

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|=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.Comment: 28+1 pp., Latex2e, 1 figur