arXiv subjects

Yves Brihaye

Publications and source records attributed to Yves Brihaye.

At least 91 records · Page 5Linked to original sources

arXiv2004

Boson stars in SU(2) Yang-Mills-scalar field theories

We present new spherically symmetric solutions of an SU(2) Einstein-Yang-Mills model coupled to a doublet of scalar fields. Sequences of asymptotically flat, Yang-Mills-boson star-type configurations are constructed numerically by considering an appropriate time-dependent ansatz for the complex scalar field and a static, purely magnetic SU(2)-Yang-Mills potential. Both nodeless as well as solutions with nodes of the scalar field and gauge potential are considered. We find that these solutions share many features with the "pure'' boson stars.

hep-th↗

arXiv2004

Gravitating Yang-Mills dyon vortices in 4+1 spacetime dimensions

We consider vortex-type solutions in $d=5$ dimensions of the Einstein gravity coupled to a nonabelian SU(2) field posessing a nonzero electric part. After the dimensional reduction, this corresponds to a $d=4$ Einstein-Yang-Mills-Higgs-U(1)-dilaton model. A general axially symmetric ansatz is presented, and the properties of the spherically symmetric solutions are analysed.

hep-th↗

arXiv2004

Spherically symmetric solutions of a (4+n)-dimensional Einstein-Yang-Mills model with cosmological constant

We construct solutions of an Einstein-Yang-Mills system including a cosmological constant in 4+n space-time dimensions, where the n-dimensional manifold associated with the extra dimensions is taken to be Ricci flat. Assuming the matter and metric fields to be independent of the n extra coordinates, a spherical symmetric Ansatz for the fields leads to a set of coupled ordinary differential equations. We find that for n > 1 only solutions with either one non-zero Higgs field or with all Higgs fields constant and zero gauge fields exist. We give the analytic solutions available in this model. These are ``embedded'' abelian solutions with a diverging size of the manifold associated with the extra n dimensions. Depending on the choice of parameters, these latter solutions either represent naked singularities or they possess a single horizon. We also present solutions of the effective 4-dimensional Einstein-Yang-Mills-Higgs-dilaton model, where the higher dimensional cosmological constant induces a Liouville-type potential. The solutions are non-abelian solutions with diverging Higgs fields, which exist only up to a maximal value of the cosmological constant.

hep-th↗

arXiv2004

Bounding Gauged Skyrmion Masses

Normally, standard (ungauged) skyrmion masses are proportional to the coupling of the Skyrme term needed for stability, and so can grow to infinite magnitude with increasing coupling. In striking contrast, when skyrmions are gauged, their masses are bounded above for any Skyrme coupling, and, instead, are of the order of monopole masses, O(v/g), so that the coupling of the Skyrme term is not very important. This boundedness phenomenon and its implications are investigated.

hep-th↗

arXiv2004

Gravity localisation in a 6-dimensional brane world

We study a 6-dimensional Einstein-Born-Infeld-Higgs model. In the limit of infinite Born-Infeld coupling, this model reduces to an Einstein-Abelian-Higgs model, in which gravity localising solutions were shown to exist. In this proceeding, we discuss further properties of the gravity localising solutions as well as of the solutions in the limit of vanishing cosmological constant.

hep-th↗

arXiv2004

Regular and black hole solutions to higher order curvature Einstein--Yang-Mills--Grassmannian systems in 5 dimensions

We construct both regular and black hole spherically symmetric solutions to the original higher curvature EYM model augmented by a Grassmannian sigma model field in $d=5$ spacetime dimensions. Unlike the original model, the new model supports regular solutions in the flat space limit. We find that a peculiar singular behaviour of the solutions in the original model, persists in the case of the modified model too. A study of the solutions to the Grassmannian model in flat space is also carried out.

hep-th↗

arXiv2004

SU(5) Gravitating Monopoles

Spherically symmetric solutions of the SU(5) Einstein-Yang-Mills-Higgs system are constructed using the harmonic map ansatz \cite{IS}. This way the problem reduces to solving a set of ordinary differential equations for the appropriate profile functions.

hep-th↗

arXiv2004

Born-Infeld strings in brane worlds

We study Born-Infeld strings in a six dimensional brane world scenario recently suggested by Giovannini, Meyer and Shaposhnikov (GMS). In the limit of the Einstein-Abelian-Higgs model, we classify the solutions found by GMS. Especially, we point out that the warped solutions, which lead to localisation of gravity, are the - by the presence of the cosmological constant - deformed inverted string solutions. Further, we construct the Born-Infeld analogues of the anti-warped solutions and determine the domain of existence of these solutions, while a analytic argument leads us to a "no-go" hypothesis: solutions which localise gravity do NOT exist in a 6 dimensional Einstein-Born-Infeld-Abelian-Higgs (EBIAH) brane world scenario. This latter hypothesis is confirmed by our numerical results.

hep-th↗

arXiv2004

Spherically symmetric Yang-Mills solutions in a (4+n)- dimensional space-time

We consider the Einstein-Yang-Mills Lagrangian in a (4+n)-dimensional space-time. Assuming the matter and metric fields to be independent of the n extra coordinates, a spherical symmetric Ansatz for the fields leads to a set of coupled ordinary differential equations. We find that for n > 1 only solutions with either one non-zero Higgs field or with all Higgs fields constant exist. We construct the analytic solutions which fulfill this conditions for arbitrary n, namely the Einstein-Maxwell-dilaton solutions. We also present generic solutions of the effective 4-dimensional Einstein-Yang-Mills-Higgs-dilaton model, which possesses n Higgs triplets coupled in a specific way to n independent dilaton fields. These solutions are the abelian Einstein-Maxwell- dilaton solutions and analytic non-abelian solutions, which have diverging Higgs fields. In addition, we construct numerically asymptotically flat and finite energy solutions for n=2.

hep-th↗

arXiv2004

Solitons on nanotubes and fullerenes as solutions of a modified non-linear Schroedinger equation

Fullerenes and nanotubes consist of a large number of carbon atoms sitting on the sites of a regular lattice. For pratical reasons it is often useful to approximate the equations on this lattice in terms of the continuous equation. At the moment, the best candidate for such an equation is the modified non-linear Schroedinger equation. In this paper, we study the modified non-linear Schroedinger equation, which arises as continuous equation in a system describing an excitation on a hexagonal lattice. This latter system can e.g. describe electron-phonon interaction on fullerene related structures such as the buckminster fullerene and nanotubes. Solutions of this modified non-linear Schroedinger equation, which have solitonic character, can be constructed using an Ansatz for the wave function, which has time and azimuthal angle dependence introduced previously in the study of spinning boson stars and Q-balls. We study these solutions on a sphere, a disc and on a cylinder. Our construction suggests that non-spinning as well as spinning solutions, which have a wave function with an arbitrary number of nodes, exist. We find that this property is closely related to the series of well-known mathematical functions, namely the Legendre functions when studying the equation on a sphere, the Bessel functions when studying the equation on a disc and the trigonometric functions, respectively, when studying the equation on a cylinder.

nlin.PS↗

arXiv2004

On linear operators with an invariant subspace of functions

Let us denote ${\cal V}$, the finite dimensional vector spaces of functions of the form $ψ(x) = p_n(x) + f(x) p_m(x)$ where $p_n(x)$ and $p_m(x)$ are arbitrary polynomials of degree at most $n$ and $m$ in the variable $x$ while $f(x)$ represents a fixed function of $x$. Conditions on $m,n$ and $f(x)$ are found such that families of linear differential operators exist which preserve ${\cal V}$. A special emphasis is accorded to the cases where the set of differential operators represents the envelopping algebra of some abstract algebra.

math-ph↗

arXiv2003

Spinning Solitons of a Modified Non-Linear Schroedinger equation

We study soliton solutions of a modified non-linear Schroedinger (MNLS) equation. Using an Ansatz for the time and azimuthal angle dependence previously considered in the studies of the spinning Q-balls, we construct multi-node solutions of MNLS as well as spinning generalisations.

hep-th↗

arXiv2003

Gravitating SU(N) Monopoles from Harmonic maps

Spherically symmetric solutions of the SU(N) Einstein-Yang-Mills-Higgs system are constructed using the harmonic map ansatz. The problem reduces to solving a set of ordinary differential equations for the appropriate profile functions. In the SU(2) case, we recover the equations studied in great detail previously, while for the SU(N) (N > 2) case we find new solutions. In the SU(3) case we see that our expressions are the gravitating analogues of the solutions obtained through the SO(3) embedding into SU(2).

hep-th↗

arXiv2003

Fullerenic solitons

We study a modified non-linear Schroedinger equation on a 2 dimensional sphere with radius R aiming to describe electron-phonon interactions on fullerenes and fullerides. These electron-phonon interactions are known to be important for the explanation of the high transition temperature of superconducting fullerides. Like in the $R\to \infty$ limit, we are able to construct non-spinning as well as spinning solutions which are characterised by the number of nodes of the wave function. These solutions are closely related to the spherical harmonic functions. For small R, we discover specific branches of the solutions. Some of the branches survive in the $R\to\infty$ limit and the solutions obtained on the plane ($R=\infty$) are recovered.

hep-th↗

arXiv2003

Spherically symmetric Yang-Mills solutions in a 5-dimensional (Anti-) de Sitter space-time

We consider an Einstein-Yang-Mills Lagrangian in a five dimensional space-time including a cosmological constant. Assuming all fields to be independent of the extra coordinate, a dimensional reduction leads to an effective (3+1)-dimensional Einstein-Yang-Mills-Higgs-dilaton model where the cosmological constant induces a Liouville potential in the dilaton field. We construct spherically symmetric solutions analytically in specific limits and study the generic solutions for vanishing dilaton coupling numerically. We find that in this latter case the solutions bifurcate with the branch of (Anti-) de Sitter-Reissner-Nordstrom ((A)dSRN) solutions.

hep-th↗

arXiv2003

de Sitter/ Anti-de Sitter global monopoles

We consider global monopoles in asymptotic de Sitter/ Anti- de Sitter space-time. We present the by our numerical analysis confirmed asymptotic behaviour of the metric and Goldstone field functions. We find that the appearance of horizons in this model depends strongly on the sign and value of the cosmological constant as well as on the value of the gravitational coupling. In Anti-de Sitter (AdS) space, we find that for a fixed value of the cosmological constant, global monopoles without horizons exist only up to a critical value of the gravitational coupling. Moreover, we observe (in contrast to another recent study) that the introduction of a cosmological constant can NOT render a positive mass of the global monopole.

hep-th↗

arXiv2003

Quasi exactly solvable (QES) equations with multiple algebraisations

We review three examples of quasi exactly solvable (QES) Hamitonians which possess multiple algebraisations. This includes the most prominent example, the Lame equation, as well as recently studied many-body Hamiltonians with Weierstrass interaction potential and finally, a 2x2 coupled channel Hamiltonian.

quant-ph↗

arXiv2003

Strings in de Sitter space

We study both global as well as local (Nielsen-Olesen) strings in de Sitter space. While these type of topological defects have been studied in the background of a de Sitter metric previously, we study here the full set of coupled equations. We find only ``closed'' solutions. The behaviour of the metric tensor of these solutions resembles that of ``supermassive'' strings with a curvature singularity at the cosmological horizon. For global strings (and the composite defect) we are able to construct solutions which are regular on the interval from the origin to the cosmological horizon if the global string core lies completely inside the horizon.

hep-th↗