Circular symmetry in the Hitchin system (original) (raw)
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New vortex solution in SU(3) gauge-Higgs theory
Physical Review D, 2000
Following a brief review of known vortex solutions in SU (N ) gauge-adjoint Higgs theories we show the existence of a new "minimal" vortex solution in SU (3) gauge theory with two adjoint Higgs bosons. At a critical coupling the vortex decouples into two abelian vortices, satisfying Bogomol'nyi type, first order, field equations. The exact value of the vortex energy (per unit length) is found in terms of the topological charge that equals to the N = 2 supersymmetric charge, at the critical coupling. The critical coupling signals the increase of the underlying supersymmetry.
An Oscillon in the SU (2) Gauged Higgs Model
We study classical dynamics in the spherical ansatz for the SU (2) gauge and Higgs fields of the electroweak Standard Model in the absence of fermions and the photon. With the Higgs boson mass equal to twice the gauge boson mass, we numerically demonstrate the existence of oscillons, extremely long-lived localized configurations that undergo regular oscillations in time. We have only seen oscillons in this reduced theory when the masses are in a two-to-one ratio. If a similar phenomenon were to persist in the full theory, it would suggest a preferred value for the Higgs mass.
Generalized self-duality for the Yang-Mills-Higgs system
Physical Review D, 2021
Self-duality is a very important concept in the study and applications of topological solitons in many areas of Physics. The rich mathematical structures underlying it lead, in many cases, to the development of exact and non-perturbative methods. We present a generalization of the Yang-Mills-Higgs system by the introduction of scalar fields assembled in a symmetric and invertible matrix h of the same dimension as the gauge group. The coupling of such new fields to the gauge and Higgs fields is made by replacing the Killing form, in the contraction of the group indices, by the matrix h in the kinetic term for the gauge fields, and by its inverse in the Higgs field kinetic term. The theory is conformally invariant in the three dimensional space IR 3. An important aspect of the model is that for practically all configurations of the gauge and Higgs fields the new scalar fields adjust themselves to solve the modified self-duality equations. We construct solutions using a spherically symmetric ansätz and show that the 't Hooft-Polyakov monopole becomes a self-dual solution of such modified Yang-Mills-Higgs system. We use an ansätz based on the conformal symmetry to construct vacuum solutions presenting non-trivial toroidal magnetic fields.
Periodic Euclidean solutions of SU(2)-Higgs theory
Physical Review D, 1999
We examine periodic, spherically symmetric, classical solutions of SU (2)-Higgs theory in four-dimensional Euclidean space. Classical perturbation theory is used to construct periodic time-dependent solutions in the neighborhood of the static sphaleron. The behavior of the action, as a function of period, changes character depending on the value of the Higgs mass. The required pattern of bifurcations of solutions as a function of Higgs mass is examined, and implications for the temperature dependence of the baryon number violation rate in the Standard Model are discussed.
Symmetric solitonic excitations of the (1+1)-dimensional Abelian-Higgs “classical vacuum”
We study the classical dynamics of the Abelian-Higgs model in (1+1) space-time dimensions bf for the case of strongly broken gauge symmetry. In this limit the wells of the potential are almost harmonic and sufficiently deep, presenting a scenario far from the associated critical point. Using a multiscale perturbation expansion, the equations of motion for the fields are reduced to a system of coupled nonlinear Schrödinger equations (CNLS). Exact solutions of the latter are used to obtain approximate analytical solutions for the full dynamics of both the gauge and Higgs field in the form of oscillons and oscillating kinks. Numerical simulations of the exact dynamics verify the validity of these solutions. We explore their persistence for a wide range of the model's single parameter which is the ratio of the Higgs mass (mH ) to the gauge field mass (mA). We show that only oscillons oscillating symmetrically with respect to the "classical vacuum", for both the gauge and the Higgs field, are long lived. Furthermore plane waves and oscillating kinks are shown to decay into oscillon-like patterns, due to the modulation instability mechanism.
Vortex solutions in nonabelian Higgs theories
Physics Letters B, 2000
A new class of vortex solutions is found in SU (2) gauge theories with two adjoint representation Higgs bosons. Implications of these new solutions and their possible connection with Center Gauge fixed pure gauge theories are discussed.
Axially symmetric solutions for SU(2) Yang–Mills theory
Journal of Mathematical Physics, 1996
By casting the Yang-Mills-Higgs equations of an SU(2) theory in the form of the Ernst equations of general relativity, it is shown how the known exact solutions of general relativity can be used to give similiar solutions for Yang-Mills theory. Thus all the known exact solutions of general relativity with axial symmetry (e.g. the Kerr metric, the Tomimatsu-Sato metric) have Yang-Mills equivalents. In this paper we only examine in detail the Kerr-like solution. It will be seen that this solution has surfaces where the gauge and scalar fields become infinite, which correspond to the infinite redshift surfaces of the normal Kerr solution. It is speculated that this feature may be connected with the confinement mechanism since any particle which carries an SU(2) color charge would tend to become trapped once it passes these surfaces. Unlike the Kerr solution, our solution apparently does not have any intrinsic angular momentum, but rather appears to give the non-Abelian field configuration associated with concentric shells of color charge.