Zalán Horváth

Grand unified schemes and spontaneous compactification

Abstract The mass spectrum of spontaneously compactified Einstein-Yang-Mills theories is computed using the Wu-Yang monopole harmonic functions. It is found that spontaneous compactification can be used to provide the correct mass scale generating the superstrong symmetry breaking which, in grand unified theories, separates quarks from leptons.

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.

Spontaneous compactification and “monopoles” in higher dimensions

Abstract Using the Wu-Yang global gauge description, the minimal gauge group is found which compactifies the extra even D dimensions into a sphere, namely SO(2N). These gauge theory solutions are associated with non-vanishing topological charges. An SO(2N) gauge theory solutions is obtained in D = 2N + 1 dimensions which describes a generalized singular magnetic monopole which conforms to the Yang definition.

Noncommutative Instantons via Dressing and Splitting Approaches

Almost all known instanton solutions in noncommutative Yang-Mills theory have been obtained in the modified ADHM scheme. In this paper we employ two alternative methods for the construction of the self-dual U(2) BPST instanton on a noncommutative euclidean four-dimensional space with self-dual noncommutativity tensor. Firstly, we use the method of dressing transformations, an iterative procedure for generating solutions from a given seed solution, and thereby generalize Belavins and Zakharovs work to the noncommutative setup. Secondly, we relate the dressing approach with Wards splitting method based on the twistor construction and rederive the solution in this context. It seems feasible to produce nonsingular noncommutative multi-instantons with these techniques.

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.

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.

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.

The Nappi-Witten string in the light-cone gauge

Some of the motivations for as well as the main points of the quantization of the Nappi-Witten string in the light-cone gauge are reviewed.

Higher level Kac-Moody representations and rank reduction in string models

Abstract It is shown that an orbifold-like construction based on an external automorphism yields the E 8 model when applied to several 10-dimensional heterotic strings. The decomposition of the internal space into direct products of level two Ĕ 8 and critical Ising representations is given. All characters and string functions of level-two Ĕ 8 representations are derived explicitly. The conformal field theory underlying the E 8 string is determined in detail. We also elucidate the role of modular invariance in the apparent uniqueness of the E 8 string.