The non-uniqueness of Yang-Mills potentials in the Coulomb gauge leads to a non-trivial vacuum structure featuring vacuum fields of both integer and half-integer topological charge. Instantons fit in consistently with this picture and their interpretation is not changed. Integer and half-integer vacua are connected by certain meron solutions and the existence of half-integer charged states appe...

We discuss new exact spherically symmetric static solutions to non-minimally extended Einstein-Yang-Mills equations. The obtained solution to the Yang-Mills subsystem is interpreted as a non-minimal Wu-Yang monopole solution. We focus on the analysis of two classes of the exact solutions to the gravitational field equations. Solutions of the first class belong to the Reissner-Nordström type, i....

Reducing Supersymmetric Yang-Mills Field Theory to a single point in the three dimensional space results in the Supersymmetric Yang-Mills Quantum Mechanics (SYMQM) which basically is the effective quantum mechanics of zero momentum modes of the original theory. Such a system is still quite non-trivial and usually inherits many properties of the original field theory. In this talk some beautiful...

We show that the 'instantonic' soliton of five-dimensional Yang-Mills theory and the closely related BPS monopole of four-dimensional Yang-Mills/Higgs theory continue to be exact static, and stable, solutions of these field theories even after the inclusion of gravitational, electromagnetic and, in the four-dimensional case, dilatonic interactions, provided that certain non-minimal interactions...

SU(3) Einstein-Yang-Mills-dilaton theory possesses sequences of static spherically symmetric sphaleron and black hole solutions for the SU(2) and the SO(3) embedding. The solutions depend on the dilaton coupling constant γ, approaching the corresponding Einstein-Yang-Mills solutions for γ → 0, and Yang-Millsdilaton solutions in flat space for γ → ∞. The sequences of solutions tend to Einstein-M...

We discuss new exact spherically symmetric static solutions to non-minimally extended Einstein-Yang-Mills equations. The obtained solution to the Yang-Mills subsystem is interpreted as a non-minimal Wu-Yang monopole solution. We focus on the analysis of two classes of the exact solutions to the gravitational field equations. Solutions of the first class belong to the Reissner-Nordström type, i....

We construct a classical mechanics Hamiltonian which exhibits spontaneous symmetry breaking akin the Coleman-Weinberg mechanism, dimensional transmutation, and asymptotically free self-similarity congruent with the beta-function of four dimensional Yang-Mills theory. Its classical equations of motion support stable periodic orbits and in a three dimensional projection these orbits are self-link...

We present a numerical method to compute path integrals in effective SU(2) Yang-Mills theories. The basic idea is to approximate the Yang-Mills path integral by summing over all gauge field configurations, which can be represented as a linear superposition of a small number of localized building blocks. With a suitable choice of building blocks many essential features of SU(2) YangMills theory ...

We give an analytical solution representing circular magnetic monopole loops joining a pair of merons in the four-dimensional Euclidean SU(2) YangMills theory. This is achieved by solving the differential equation for the adjoint color (magnetic monopole) field in the two–meron background field within the recently developed reformulation of the Yang-Mills theory. Our analytical solution corresp...

To verify the conjecture that Yang-Mills theory in the infrared limit is equivalent to a spin system whose excitations are knot solitons, a numerical algorithm based on the inverse Monte Carlo method is proposed. To investigate the stability of the effective spin field action, numerical studies of the renormalization group flow for the coupling constants are suggested. A universality of the eff...