arXiv subjects
Publications and source records attributed to Betti Hartmann.
We study the spectrum of fermionic modes on cosmic string loops. We find no fermionic zero modes nor massive bound states - this implies that vortons stabilized by fermionic currents do not exist. We have also studied kink-(anti)kink and vortex-(anti)vortex systems and find that all systems that have vanishing net topological charge do not support fermionic bound modes.
We discuss magnetic monopole solutions of the Einstein-Yang-Mills-Higgs equations with a positive cosmological constant. These configurations approach asymptotically the de Sitter spacetime background and exist only for a nonzero Higgs potential. We find that the total mass of the solutions within the cosmological horizon is finite. However, their mass evaluated by using the surface counterterm method outside the cosmological horizon at early/late time infinity generically diverges. Magnetic monopole solutions with finite mass and noninteger charge are found however in a truncation of the theory with a vanishing Higgs field. Both solutions with a regular origin and cosmological black holes are studied, special attention being paid to the computation of the global charges.
We study the non-linear Schroedinger equation in (1+1) dimensions in which the nonlinear term is taken in the form of a nonlocal interaction of the Coulomb or Yukawa-type. We solve the equation numerically and find that, for all values of the nonlocal coupling constant, and in all cases, the equation possesses solitonic solutions. We show that our results, for the dependence of the height of the soliton on the coupling constant, are in good agreement with the predictions based on an analytic treatment in which the soliton is approximated by a gaussian.
We consider global monopoles as well as black holes with global monopole hair in Einstein-Goldstone model with a cosmological constant in four spacetime dimensions. Similar to the $Λ=0$ case, the mass of these solutions defined in the standard way diverges. We use a boundary counterterm subtraction method to compute the mass and action of $Λ\neq 0$ configurations. The mass of the asymptotically de Sitter solutions computed in this way turns out to take positive values in a specific parameter range and, for a relaxed set of asymptotic boundary conditions, yields a counterexample to the maximal mass conjecture.
We study a 7-dimensional brane world scenario with a Ricci-flat 3-brane residing in the core of a composite monopole defect, i.e. a defect composed of a 'tHooft-Polyakov and a global monopole. Admitting a direct interaction between the two bosonic sectors of the theory, we analyse the structure of the space-time in the limits of small, respectively large direct interaction coupling constant. For large direct interaction, the global monopole disappears from the system and leaves behind a negative cosmological constant in the bulk such that gravity-localising solutions are possible without the a priori introduction of a bulk cosmological constant.
We construct the first examples of deformed non-abelian black strings in a 5-dimensional Einstein-Yang-Mills model. Assuming all fields to be independent of the extra coordinate, we construct deformed black strings, which in the 4-dimensional picture correspond to axially symmetric non-abelian black holes in gravity-dilaton theory. These solutions thus have deformed S^2 x R horizon topology. We study fundamental properties of the black strings and find that for all choices of the gravitational coupling two branches of solutions exist. The limiting behaviour of the second branch of solutions however depends strongly on the choice of the gravitational coupling.
We consider the Abelian Higgs model in a (p+2)-dimensional space time with topology M^{p+1} x S^1 as a field theoretical toy model for tachyon condensation on Dp-branes. The theory has periodic sphaleron solutions with the normal mode equations resembling Lame-type equations. These equations are quasi-exactly solvable (QES) for specific choices of the Higgs- to gauge boson mass ratio and hence a finite number of algebraic normal modes can be computed explicitely. We calculate the tachyon potential for two different values of the Higgs- to gauge boson mass ratio and show that in comparison to previously studied pure scalar field models an exact cancellation between the negative energy contribution at the minimum of the tachyon potential and the brane tension is possible for the simplest truncation in the expansion about the field around the sphaleron. This gives further evidence for the correctness of Sen's conjecture.
We consider solutions of the Yang-Mills-Higgs system coupled to gravity in asymptotically de Sitter spacetime. The basic features of two classes of solutions are discussed, one of them corresponding to magnetic monopoles, the other one to sphalerons. We find that although the total mass within the cosmological horizon of these configurations is finite, their mass evaluated at timelike infinity generically diverges. Also, no solutions exist in the absence of a Higgs potential.
We study static, spherically symmetric, composite global-local monopoles with a direct interaction term between the two sectors in the regime where the interaction potential is large. At some critical coupling the global defect disappears and with it the deficit angle of the space-time. We find new solutions which represent local monopoles in an Anti-de-Sitter spacetime. In another parameter range the magnetic monopole, or even both, disappear. The decay of the magnetic monopole is accompanied by a dynamical transition from the higgsed phase to the gauge-symmetric phase. We comment on the applications to cosmology, topological inflation and braneworlds.
We study vortex-type solutions in a (4+1)-dimensional Einstein-Yang-Mills-SU(2) model. Assuming all fields to be independent on the extra coordinate, these solutions correspond in a four dimensional picture to axially symmetric multimonopoles, respectively monopole-antimonopole solutions. By boosting the five dimensional purely magnetic solutions we find new configurations which in four dimensions represents rotating regular nonabelian solutions with an additional electric charge.
We study solitons arising in a system describing the interaction of a two-dimensional discrete hexagonal lattice with an additional electron field (or, in general, an exciton field). We assume that this interaction is electron-phonon-like. In our previous paper [4], we have studied the existence of two-dimensional solitons and have found that these solitons exist only if the electron-phonon coupling constant is sufficiently large. In this paper, we report the results of our investigation for small values of this constant, close to its critical value for the existence of solitons. We find that as the coupling decreases the soliton gets very broad and then becomes effectively one-dimensional.
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.
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.
Non-abelian black strings in a 5-dimensional Einstein-Yang-Mills model are considered. The solutions are spherically symmetric non-abelian black holes in 4 dimensions extended into an extra dimension and thus possess horizon topology S^2 x R. We find that several branches of solutions exist. In addition, we determine the domain of existence of the non-abelian black strings.
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.
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.
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.
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.