Multimonopoles and closed vortices in SU(2) Yang-Mills-Higgs theory

We review classical monopole solutions of the SU(2) Yang-Mills-Higgs theory. The first part is a pedagogical introduction into to the basic features of the celebrated 't Hooft - Polyakov monopole. In the second part we describe new classes of static axially symmetric solutions which generalise 't Hooft - Polyakov monopole. These configurations are either deformations of the topologically trivial sector or the sectors with different topological charges. In both situations we construct the solutions representing the chains of monopoles and antimonopoles in static equilibrium. The solutions of another type are closed vortices which are centred around the symmetry axis and form different bound systems. Configurations of the third type are monopoles bounded with vortices. We suggest classification of these solutions which is related with 2d Poincare index.Comment: 34 pages, 8 figures. Invited contribution prepared for Review Volume "Etudes on Theoretical Physics" dedicated to 65th anniversary of the Department of Theoretical Physics, Belarus State University, Minsk. Based on a work in collaboration with Jutta Kunz and Burkhard Kleihaus. Any comments and suggestions, especially with respect to references, are welcom

The Color--Flavor Transformation of induced QCD

The color-flavor transformation is applied to the U(N) lattice gauge model, in which the gauge theory is induced by a heavy chiral scalar field sitting on lattice sites. The flavor degrees of freedom can encompass several `generations' of the auxiliary field, and for each generation, remaining indices are associated with the elementary plaquettes touching the lattice site. The effective, color-flavor transformed theory is expressed in terms of gauge singlet matrix fields carried by lattice links. The effective action is analyzed for a hypercubic lattice in arbitrary dimension. The saddle points equations of the model in the large-N limit are discussed.Comment: 16 pages, 4 eps figures. Talk given by the second author at the 5th International Conference "Quark confinement and the hadron spectrum", Gargnano, Garda Lake, 10-14 September 200

Transitions between Vortex Rings and Monopole-Antimonopole Chains

In monopole-antimonopole chain solutions of SU(2) Yang-Mills-Higgs theory the Higgs field vanishes at m isolated points along the symmetry axis, whereas in vortex ring solutions the Higgs field vanishes along one or more rings, centered around the symmetry axis. We investigate how these static axially symmetric solutions depend on the strength of the Higgs selfcoupling \lambda. We show, that as the coupling is getting large, new branches of solutions appear at critical values of \lambda. Exhibiting a different node structure, these give rise to transitions between vortex rings and monopole-antimonopole chains.Comment: 14 pages, 18 figures, published in pl

Non-Abelian fields in AdS4_4 spacetime: axially symmetric, composite configurations

We construct new finite energy regular solutions in Einstein-Yang-Mills-SU(2) theory. They are static, axially symmetric and approach at infinity the anti-de Sitter spacetime background. These configurations are characterized by a pair of integers $(m, n)$, where $m$ is related to the polar angle and $n$ to the azimuthal angle, being related to the known flat space monopole-antimonopole chains and vortex rings. Generically, they describe composite configurations with several individual components, possesing a nonzero magnetic charge, even in the absence of a Higgs field. Such Yang-Mills configurations exist already in the probe limit, the AdS geometry supplying the attractive force needed to balance the repulsive force of Yang-Mills gauge interactions. The gravitating solutions are constructed by numerically solving the elliptic Einstein-DeTurck--Yang-Mills equations. The variation of the gravitational coupling constant $\alpha$ reveals the existence of two branches of gravitating solutions which bifurcate at some critical value of $\alpha$. The lower energy branch connects to the solutions in the global AdS spacetime, while the upper branch is linked to the generalized Bartnik-McKinnon solutions in asymptotically flat spacetime. Also, a spherically symmetric, closed form solution is found as a perturbation around the globally anti-de Sitter vacuum state.Comment: 30 pages, 15 figure

Gravitating Monopole-Antimonopole Systems at Large Scalar Coupling

We discuss static axially symmetric solutions of SU(2) Einstein-Yang-Mills-Higgs theory for large scalar coupling. These regular asymptotically flat solutions represent monopole-antimonopole chain and vortex ring solutions, as well as new configurations, present only for larger values of the scalar coupling. When gravity is coupled to the Yang-Mills-Higgs system, branches of gravitating solutions emerge from the flat-space solutions, and extend up to critical values of the gravitational coupling constant. For small scalar coupling only two branches of gravitating solutions exist, where the second branch connects to a generalized Bartnik-McKinnon solution. For large scalar coupling, however, a plethora of gravitating branches can be present and indicate the emergence of new flat-space branches.Comment: 29 pages, 13 figure

Axially symmetric Yang-Mills-Higgs solutions in AdS spacetime

We consider axially symmetric solutions of SU(2) Yang-Mills-Higgs theory in globally AdS spacetime and a fixed Schwarzschild-AdS black hole background. The solutions are characterized by two integers $(m,n)$ where $m$ is related to the polar angle and $n$ to the azimuthal angle. Two types of finite energy, regular configurations are considered: solutions with net magnetic charge $n>1$ and monopole-antimonopole pairs and chains with zero net magnetic charge. The configurations are endowed with an electric charge and carry also a nonvanishing angular momentum density.Comment: 13 pages, 3 figure