26 research outputs found

### 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 AdS$_4$ 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

### 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

### 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