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

Monopoles in the Abelian Projection of Gluodynamics

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.Comment: 13 pages, 7 eps figures, LaTeX using PTPTEX.sty (included); Lectures given by M.I.Polikarpov at the 1997 Yukawa International Seminar on "Non-perturbative QCD - Structure of QCD Vacuum -" (YKIS'97), 2-12 December, 1997, Yukawa Institute for Theoretical Physics, Kyoto, Japa

A novel probe of the vacuum of the lattice gluodynamics

We introduce a notion of minimal number of negative links on the lattice for a given original configuration of SU(2) fields. Negative links correspond to a large potential, not necessarily large action. The idea is that the minimal number of negative links is a gauge invariant notion. To check this hypothesis we measure correlator of two negative links, averaged over all the directions, as function of the distance between the links. The inverse correlation length coincides within the error bars with the lightest glueball mass.Comment: 6 pages, 2 figure