arXiv subjects
Publications and source records attributed to Yves Brihaye.
We construct globally regular as well as non-abelian black hole solutions of a higher order curvature Einstein-Yang-Mills (EYM) model in $d=5$ dimensions. This model consists of the superposition of the first two members of the gravitational hierarchy (Einstein plus first Gauss-Bonnet(GB)) interacting with the superposition of the first two members of the $SO(d)$ Yang--Mills hierarchy.
Recently, Gomez-Ullate et al. (1) have studied a particular N-particle quantum problem with an elliptic function potential supplemented by an external field. They have shown that the Hamiltonian operator preserves a finite dimensional space of functions and as such is quasi exactly solvable (QES). In this paper we show that other types of invariant function spaces exist, which are in close relation to the algebraic properties of the elliptic functions. Accordingly, series of new algebraic eigenfunctions can be constructed.
Linear operators preserving the direct sum of polynomial rings P(m)\oplus P(n) are constructed. In the case |m-n|=1 they correspond to atypical representations of the superalgebra osp(2,2). For |m-n|=2 the generic, finite dimensional representations of the superalgebra q(2) are recovered. An example of a Hamiltonian possessing such a hidden algebra is analyzed.
We construct spherically and axially symmetric monopoles in SU(5) Yang-Mills-Higgs theory both in flat and curved space as well as spherical and axial non-abelian, ''hairy'' black holes. We find that in analogy to the SU(2) case, the flat space monopoles are either non-interacting (in the BPS limit) or repelling. In curved space, however, gravity is able to overcome the repulsion for suitable choices of the Higgs coupling constants and the gravitational coupling. In addition, we confirm that indeed all qualitative features of (gravitating) SU(2) monopoles are found as well in the SU(5) case. For the non-abelian black holes, we compare the behaviour of the solutions in the BPS limit with that for non-vanishing Higgs self-coupling constants.
Considering a Skyrme model with a peculiar gauging of the symmetry, monopole-like solutions exist through a topological lower bound. However, it was recently shown that these objects cannot form bound states in the limit of vanishing Skyrme coupling. Here we consider these monopoles in scalar-tensor gravity. A numerical study of the equations reveals that neither the coupling to gravity nor to the scalar dilaton nor to dilaton-gravity leads to bound multimonopole states.
We study the direct interaction between global and local monopoles. While in two previous papers, the coupling between the two sectors was only indirect through the coupling to gravity, we here introduce a new term in the potential that couples the Goldstone field and the Higgs field directly. We investigate the influence of this term in curved space and compare it to the results obtained previously.
We present a numerical study of critical phenomena (including the Lue-Weinberg phenomenon) arising for gravitating monopoles in a global monopole spacetime. The equations of this model have been recently studied by Spinelly et al. in a domain of parameter space away from the critical points.
We consider the Abelian Higgs model as well as the SU(2) Georgi-Glashow model in which the gauge field action is replaced by a non linear Born-Infeld action. We study soliton solutions arising in these models, namely the vortex and monopole solutions, respectively. We construct formulas which provide good approximations for the mass of the Born-Infeld deformed solitons using only the data of the undeformed solutions. The results obtained indicate that in the self-dual limit, the Born-Infeld interaction leads to bound vortices, while for monopoles it gives rise to repulsion.
We study spherically and axially symmetric monopoles of the SU(2) Einstein-Yang-Mills-Higgs-dilaton (EYMHD) system with a new coupling between the dilaton field and the covariant derivative of the Higgs field. This coupling arises in the study of (4+1)-dimensional vortices in the Einstein-Yang-Mills (EYM) system.
We study axially symmetric monopoles of both the SU(2) Yang-Mills-Higgs-Dilaton (YMHD) as well as of the SU(2) Einstein-Yang-Mills-Higgs-Dilaton (EYMHD) system. We find that equally to gravity, the presence of the dilaton field can render an attractive phase. We also study the influence of a massive dilaton on the attractive phase in the YMHD system.
We study the SU(2) electroweak model in which the standard Yang-Mills coupling is supplemented by a Born-Infeld term. The deformation of the sphaleron and bisphaleron solutions due to the Born-Infeld term is investigated and new branches of solutions are exhibited. Especially, we find a new branch of solutions connecting the Born-Infeld sphaleron to the first solution of the Kerner-Gal'tsov series.
We study gravitating monopoles and non-abelian black holes of SU(2) Einstein-Yang-Mills-Higgs theory coupled to a massless dilaton. The domain of existence of these solutions decreases with increasing dilaton coupling constant. The critical solutions of this system are Einstein-Maxwell-dilaton solutions.
New examples of matrix quasi exactly solvable Schroedinger operators are constructed. One of them constitutes a matrix generalization of the quasi exactly solvable anharmonic oscillator, the corresponding invariant vector space is constructed explicitely. Also investigated are matrix generalizations of the Lame equation.
Three dimensional SO(3) gauged Skyrme models characterised by specific potentials imposing special asymptotic values on the chiral field are considered. These models are shown to support finite energy solutions with nonvanishing magnetic and electrix flux, whose energies are bounded from below by two distinct charges - the magnetic (monopole) charge and a non-integer version of the Baryon charge. Unit magnetic charge solutions are constructed numerically and their properties characterised by the chosen asymptotics and the Skyrme coupling are studied. For a particular value of the chosen asymptotics, charge-2 axially symmetric solutions are also constructed and the attractive nature of the like-monopoles of this system are exhibited. As an indication towards the possible existence of large clumps of monopoles, some consideration is given to axially symmetric monopoles of charges-2,3,4.
A non-linear sigma model mimicking the Skyrme model on S_3 is proposed and a family of classical solutions to the equations are constructed numerically. The solutions terminate into catastrophe-like spikes at critical values of the Skyrme coupling constant and, when this constant is zero, they coincide with the series of Harmonic maps on S_3 constructed some years ago by P. Bizon.
We study static spherically symmetric gravitating dyon solutions and dyonic black holes in Einstein-Yang-Mills-Higgs theory. The gravitating dyon solutions share many features with the gravitating monopole solutions. In particular, gravitating dyon solutions and dyonic black holes exist up to a maximal coupling constant, and beside the fundamental dyon solutions there are excited dyon solutions.
Series of finite dimensional representations of the superalgebras spl(p,q) can be formulated in terms of linear differential operators acting on a suitable space of polynomials. We sketch the general ingredients necessary to construct these representations and present examples related to spl(2,1) and spl(2,2). By revisiting the products of projectivised representations of sl(2), we are able to construct new sets of differential operators preserving some space of polynomials in two or more variables. In particular, this allows to express the representation of spl(2,1) in terms of matrix differential operators in two variables. The corresponding operators provide the building blocks for the construction of quasi exactly solvable systems of two and four equations in two variables. We also present a quommutator deformation of spl(2,1) which, by construction, provides an appropriate basis for analyzing the quasi exactly solvable systems of finite difference equations.
We reconsider the quasi exactly solvable matrix models constructed recently by R. Zhdanov. The 2$\times$2 matrix operators representing the algebra sl(2) are generalized to matrices of arbitrary dimension and a similar construction is achieved for the algebra sl(n).