Péter Forgács

Gravitating monopole solutions

Abstract We present analytical and numerical results for static, spherically symmetric solutions of the Einstein-Yang-Mills-Higgs equations corresponding to magnetic monopoles and non-abelian magnetically charged black holes. In the limit of infinite Higgs mass we give an existence proof for these solutions. The stability of the abelian extremal Reissner-Nordstrom black holes is reanalyzed.

Exact multimonopole solutions in the Bogomolny-Prasad-Sommerfied limit

Abstract A systematic method for generating axially symmetric multimonopole solutions is presented. The Bogomolny-Prasad-Sommerfield one monopole and a new doubly charged monopole are obtained via Harrisons Backlund transformation.

A new family of SU(2) symmetric integrable sigma models

Abstract Local Lagrangians are derived for a class of SU (2) invariant sigma models admitting two commuting Kac-Moody algebras at the level of Poisson brackets. The one-loop renormalizability of these models is established. Some hueristic arguments are presented in favour of their quantum integrability.

Dimensional reduction of gauge theories yielding unified models spontaneously broken to SU3×U1

By dimensional reduction of pure gauge theories (with gauge groupG) over a compact coset spaceS/R, one obtains four-dimensional theories where scalar fields and a symmetry breaking potential appear naturally. We present an analysis of all such unified models with simpleG which are spontaneously broken toSU3×SU2×U1, and which can be obtained by this technique with the added restriction thatS⊂G. Although the bosonic sectors appear promising, no cases are found with the correct quantum numbers for the surviving fermions.

Non-linear superposition of monopoles

Abstract With the aid of Backlund transformations we construct exact multimonopole solutions of the axially and mirror symmetric Bogomolny equations. The explicit form of the length of the Higgs field is given and is studied both analytically and numerically. The energy density for monopoles with charges 2, 3, 5 is also calculated.

Twisted superconducting semilocal strings

Abstract A new class of twisted, current carrying, stationary , straight string solutions having finite energy per unit length is constructed numerically in an extended Abelian Higgs model with global SU ( 2 ) symmetry. The new solutions correspond to deformations of the embedded Abrikosov–Nielsen–Olesen (ANO) vortices by a twist—a relative coordinate dependent phase between the two Higgs fields. The twist induces a global current flowing through the string, and the deformed solutions bifurcate with the ANO vortices in the limit of vanishing current. For each value of the winding number n = 1 , 2 , … (determining the magnetic flux through the plane orthogonal to the string) there are n distinct, two-parametric families of solutions. One of the continuously varying parameters is the twist, or the corresponding current, the other one can be chosen to be the momentum of the string. For fixed values of the momentum and twist, the n distinct solutions have different energies and can be viewed as a lowest energy “fundamental” string and its n − 1 “excitations” characterized by different values of their “polarization”. The latter is defined as the ratio of the angular momentum of the vortex and its momentum. In their rest frame the twisted vortices have lower energy than the embedded ANO vortices and could be of considerable importance in various physical systems (from condensed matter to cosmic strings).

Solution-generating technique for self-dual monopoles

Abstract A solution generating method based on the linearization of the self-duality (Bogomolny) equations of SU( N ) gauge theories is described in detail. We point out its connection to matrix Riemann-Hilbert problems and to the Atiyah-Ward ansatze. We show how the multi-monopoles can be constructed with our method. We also investigate the energy density of the separated SU(2) two-monopole solutions.

Dimensional Reduction and Dynamical Symmetry Breaking

Abstract We present a model in which the electroweak gauge group is broken according to a dynamical scenario based on the chiral symmetry breaking of high colour representations. The dynamical scenario requires also the existence of elementary Higgs fields, which in the present scheme come from the dimensional reduction of a pure gauge theory.

Topology and saddle points in field theories

Abstract We point out that in a large class of models there are non-contractible loops in configuration space. This signals the possible existence of static, finite energy saddle points. We show that these solutions play a role in the tunnelling process.

Classification of static, spherically symmetric solutions of the Einstein-Yang-mills theory with positive cosmological constant

We give a complete classification of all static, spherically symmetric solutions of the SU(2) Einstein-Yang-Mills theory with a positive cosmological constant. Our classification proceeds in two steps. We first extend solutions of the radial field equations to their maximal interval of existence. In a second step we determine the Carter-Penrose diagrams of all 4-dimensional space-times constructible from such radial pieces. Based on numerical studies we sketch a complete phase space picture of all solutions with a regular origin.