Black hole superradiance, which only relies on gravitational interactions, can provide a powerful probe of the existence of ultralight bosons that are weakly coupled to ordinary matter. However, as a boson cloud grows through superradiance, nonlinear effects from interactions with itself or other fields may become important. As a representative example of this, we use nonlinear evolutions to study black hole superradiance of a vector boson that attains a mass, via a coupling to a complex scalar, through the Higgs mechanism. For the cases considered, we find that the superradiant instability can lead to a transient period where the scalar field reaches its symmetry restoration value, leading to the formation of closed vortex strings, the temporary disruption of the exponential growth of the cloud, and an explosive outburst of energy. After the cloud loses sufficient mass, the superradiant growth resumes, and the cycle repeats. Thus, the black hole will be spun down but, potentially, at a much lower rate compared to when nonlinear effects are unimportant, and with the liberated energy going primarily into bosonic radiation instead of gravitational waves.
Vortices and black holes set the scene for many interesting dynamical processes in physics. Here, we study the dynamical instability of quantised vortices and rotational superradiance around rotating black holes, illustrating in the process that the same physics is at play in these two seemingly disparate phenomena. We also compare the instability of the vortex to the black hole bomb instability, which occurs for massive scalar fields in the Kerr spacetime. Taking inspiration from the analogy between black hole bomb modes and the hydrogen spectrum, the vortex instability is compared with nucle…
We study the formation and evolution of vortices in $U(1)$ dark photon dark matter and dark photon clouds that arise through black hole superradiance. We show how the production of both longitudinal mode and transverse mode dark photon dark matter can lead to the formation of vortices. After vortex formation, the energy stored in the dark photon dark matter will be transformed into a large number of vortex strings, eradicating the coherent dark photon dark matter field. In the case where a dark photon magnetic field is produced, bundles of vortex strings are formed in a superheated phase trans…
The static vortex solution in Abelian Higgs model with small ratio of vector and Higgs particle masses is considered. Several formulae approximating this solution are discussed. The accuracy of these approximations is tested by numerical computations.
Using the Abelian Higgs model, we study the radial excitations of single vortex and their propagation modes along the vortex line. We call such beyond-stringy modes {\it peristaltic} modes of single vortex. With the profile of the static vortex, we derive the vortex-induced potential, i.e., single-particle potential for the Higgs and the photon field fluctuations around the static vortex, and investigate the coherently propagating fluctuations which corresponds to the vibration of the vortex. We derive, analyze and numerically solve the field equations of the Higgs and the photon field fluctua…
Classical vortex solutions in $(1+2)$-dimensional multi-Higgs systems are studied. In particular the existence of such a solution requires equal characteristic lengths and a specific relation between the ratio of the two Higgs vacuum expectation values and the couplings in the Higgs potential, if $λ_3\neq 0$.
We study vortex solutions in a theory with dynamics governed by two weakly coupled Abelian Higgs models, describing a hidden sector and a visible sector. We analyze the radial dependence of the axially symmetric solutions constructed numerically and discuss the stability of vortex configurations for different values of the model parameters, studying in detail vortex decay into lower energy configurations. We find that even in a weak coupling regime vortex solutions strongly depend on the parameters of both the visible and hidden sectors. We also discuss on qualitative grounds possible implicat…
Local correlations of Z-vortex operators with gauge and Higgs fields (lattice quantum vortex profiles) as well as vortex two-point functions are studied in the crossover region near a Higgs mass of 100 GeV within the 3D SU(2) Higgs model. The vortex profiles resemble certain features of the classical vortex solutions in the continuum. The vortex-vortex interactions are analogous to the interactions of Abrikosov vortices in a type-I superconductor.
We analyze the existence of string-like defects in a two-Higgs-doublet system having $SU(2) \times U(1)_Y \times U(1)_{Y^{\prime}}$ as gauge group. We are able to show that, when certain relations among the parameters hold, these configurations satisfy a set of first order differential equations (Bogomol'nyi equations) and their energy is proportional to their topological charge.}
Classical vortex solutions in various two-Higgs systems are studied. The systems we consider include the standard model with two Higgs doublets, in which case the vortex appears as part of a string-like object. The Higgs potentials contain several different couplings in general and the spontaneous symmetry breaking involves with two different vacuum expectation values. In particular it is shown that the existence of such a solution in general requires a specific ratio of the two Higgs vacuum expectation values, i.e. $\tanβ$, and some inequalities between different Higgs couplings. This ratio c…
The contribution of nontrivial vacuum (topological) excitations, more specifically vortex configurations of the self-dual Chern-Simons-Higgs model, to the functional partition function is considered. By using a duality transformation, we arrive at a representation of the partition function in terms of which explicit vortex degrees of freedom are coupled to a dual gauge field. By matching the obtained action to a field theory for the vortices, the physical properties of the model in the presence of vortex excitations are then studied. In terms of this field theory for vortices in the self-dual …
Vortex solutions are topologically stable field configurations that can play an important role in condensed matter, field theory, and cosmology. We investigate vortex configuration in a 2+1 dimensional Abelian Higgs theory supplemented by higher order derivative self-interactions, related with Galileons. Our vortex solutions have features that make them qualitatively different from well-known Abrikosov-Nielsen-Olesen configurations, since the derivative interactions turn on gauge invariant field profiles that break axial symmetry. By promoting the system to a 3+1 dimensional string configurati…
We use lattice Monte Carlo simulations to study non-perturbatively the tension, i.e. the free energy per unit length, of an infinitely long vortex in the three-dimensional U(1)+Higgs theory. This theory is the low-energy effective theory of high-temperature scalar electrodynamics, the standard framework for cosmic string studies. The vortex tension is measured as a function of the mass parameter at a large value of the Higgs self-coupling, where the transition between the phases is continuous. It is shown that the tension gives an order parameter that can distinguish between the two phases of …
We find evidence for the existence of solutions of the Einstein and Abelian Higgs field equations describing a black hole pierced by a Nielsen-Olesen vortex. This situation falls outside the scope of the usual no-hair arguments due to the non-trivial topology of the vortex configuration and the special properties of its energy-momentum tensor. By a combination of numerical and perturbative techniques we conclude that the black hole horizon has no difficulty in supporting the long range fields of the Nielsen Olesen string. Moreover, the effect of the vortex can in principle be measured from inf…
This work deals with the presence of analytical vortex configurations in generalized models of the Maxwell-Higgs type in the three-dimensional spacetime. We implement a procedure that allows to decouple the first order equations, which we use to solve the model analytically. The approach is exemplified with three distinct models that show the robustness of the construction. In the third model, one finds analytical solutions that exhibit interesting compact vortex behavior.
Vortex configurations in the electroweak gauge theory are investigated. Two gauge-inequivalent solutions of the field equations, the Z and W vortices, have previously been found. They correspond to embeddings of the abelian Nielsen-Olesen vortex solution into a U(1) subgroup of SU(2)xU(1). It is shown here that any electroweak vortex solution can be mapped into a solution of the same energy with a vanishing upper component of the Higgs field. The correspondence is a gauge equivalence for all vortex solutions except those for which the winding numbers of the upper and lower Higgs components add…
The stability of an abelian (Nielsen-Olesen) vortex embedded in the electroweak theory against W production is investigated in a gauge defined by the condition of a single-component Higgs field. The model is characterized by the parameters $β=({M_H\over M_Z})^2$ and $γ=\cos^2θ_{\rm w}$ where $θ_{\rm w}$ is the weak mixing angle. It is shown that the equations for W's in the background of the Nielsen-Olesen vortex have no solutions in the linear approximation. A necessary condition for the nonlinear equations to have a solution in the region of parameter space where the abelian vortex is classi…
The confining and topological properties of the compact Abelian Higgs model with doubly-charged Higgs field in three space-time dimensions are studied. We consider the London limit of the model. We show that the monopoles are forming chain-like structures (kept together by ANO vortices) the presence of which is essential for getting simultaneously permanent confinement of singly-charged particles and breaking of the string spanned between doubly-charged particles. In the confinement phase the chains are forming percolating clusters while in the deconfinement (Higgs) phase the chains are of fin…
We study the statistical properties of Z-vortices and Nambu monopoles in the 3D SU(2) Higgs model for a Higgs mass M_H \approx 100 GeV near and above the crossover temperature, where these defects are thermally excited. Although there is no phase transition at that strong selfcoupling, we observe that the Z-vortices exhibit the percolation transition that has been found recently to accompany the first order thermal transition that exists at smaller Higgs mass. Above the crossover temperature percolating networks of Z-vortex lines are ubiquitous, whereas vortices form a dilute gas of closed vor…
New solutions to the abelian U(1) Higgs model, corresponding to vortices of integer and half-integer winding number bound onto the edges of domain walls and possibly surrounded by annular current flows, are described, based on a fine-grained analysis of the topology of such configurations in spacetime. The existence of these states, which saturate BPS bounds in specific limits and are quite reminiscent of D-branes and membranes in general, could have interesting and some important consequences in a wide range of physical contexts. For instance, they raise the possibility that for some regimes …
Excitations of a vortex are usually considered in a linear approximation neglecting their backreaction on the vortex. In the present paper we investigate backreaction of Proca type excitations on a straightlinear vortex in the Abelian Higgs model. We propose exact Ansatz for fields of the excited vortex. From initial set of six nonlinear field equations we obtain (in a limit of weak excitations) two linear wave equations for the backreaction corrections. Their approximate solutions are found in the cases of plane wave and wave packet type excitations. We find that the excited vortex radiates v…
Semilocal strings are vortices in the extended Abelian-Higgs model with two complex Higgs scalar fields among which a global $SU(2)$ symmetry acts. They are known to be stable (unstable against expansion) in type-I (II) superconductors, in which gauge field is heavier (lighter) than the Higgs scalar field. In this paper, we find that vortices can be stabilized in the whole parameter region including the type-II region by adding a potential term breaking the $SU(2)$ symmetry. We construct numerical solutions in various parameters and determine the vortex phase diagram consisting of six phases. …
Vortices are considered in relativistic Maxwell-Higgs systems in interaction with a neutral scalar field. The gauge field interacts with the neutral field via the presence of generalized permeability, and the charged and neutral scalar fields interact in a way dictated by the presence of first order differential equations that solve the equations of motion. The neutral field may be seen as the source field of the vortex, and we study some possibilities, which modify the standard Maxwell-Higgs solution and include internal structure to the vortex.
We modify the standard Abelian-Higgs model by introducing spatially-dependent couplings for the scalar and vector fields. We investigate static, non-cylindrically symmetric solutions of the resulting field equations and propose a pinch solution which interpolates between degenerate vacua along the string, labelled by $\pm |n|$. This configuration corresponds to a vortex which shrinks to Planck scale before re-emerging as an anti-vortex, resulting in the formation of a bead pair with one bead at either side of the intersection. The solution is then topologically stable. A key assumption is that…
We determine the contribution of nontrivial vacuum (topological) excitations, more specifically vortex--strings of the Abelian Higgs model in 3+1 dimensions, to the functional partition function. By expressing the original action in terms of dual transformed fields we make explicit in the equivalent action the contribution of the vortex--strings excitations of the model. The effective potential of an appropriately defined local vacuum expectation value of the vortex--string field in the dual transformed action is then evaluated both at zero and finite temperatures and its properties discussed …
Real time rearrangement of particle spectra is studied numerically in a U(1) Gauge+Higgs system, in the unitary gauge and in three spatial dimensions. The cold system starts from the symmetric phase. Evolution of the partial energy densities and pressures reveal well-defined equations of state for the longitudinal and transversal gauge fields very early. Longitudinal modes are excited more efficiently and thermalize the slowest. Hausdorff-dimension of the Higgs-defect manifold, eventually seeding vortex excitations is thoroughly discussed. Scaling dependence of the vortex density on the charac…
Numerical data for the SU(2) confining string in the maximal abelian projection are analysed. The distribution of the electric flux and monopole currents are perfectly described by the classical equations of motion for the dual Abelian Higgs model. The mass of the vector boson is equal to the mass of the monopole (Higgs particle) within numerical errors. The classical energy per unit length of the Abrikosov vortex reproduces 94% of the full non-Abelian string tension.
We perform a path-integral analysis of the string representation of the dual Abelian Higgs (DAH) model beyond the London limit, where the string describing the vortex of a flux tube has a finite thickness. We show that besides an additional vortex core contribution to the string tension, a modified Yukawa interaction appears as a boundary contribution in the type-II dual superconducting vacuum. In the London limit, the modified Yukawa interaction is reduced to the Yukawa one.
We find that a $Z$-string is stable in a wide range of parameter space of the two Higgs doublet model due to a split into a pair of two topological $Z$-strings with fractional $Z$ fluxes. This configuration, a bound state of the two strings connected by a domain wall, is called a vortex molecule. Although the vortex molecule has no net topological charge, the locally induced topological charge density is polarized, namely distributed positively around one constituent string and negatively around the other constituent string, leading to the stability of the molecule. We numerically show that th…
We study properties of Z-vortices in the crossover region of the 3D SU(2) Higgs model. Correlators of the vortex currents with gauge field energy and Higgs field squared ("quantum vortex profile") reveal a structure that can be compared with a classical vortex. We define a core size and a penetration depth from the vortex profile. Z-vortices are found to interact with each other analogously to Abrikosov vortices in a type-I superconductor.
We investigate numerically the properties of the Abrikosov-Nielsen-Olesen strings in 4D abelian Higgs model. The fractal dimension D_f of the vortex strings was found to be large in the Coulomb phase and it is close to 2 in the Higgs phase. We also show that the Wilson loop for non-integer charges is correlated with the linking number of the vortex string world sheets and the test particle world trajectory. We find that this topological (Aharonov-Bohm) interaction gives the main contribution to the Wilson loop quantum average for non-integer test charges in the vicinity of the Coulomb-Higgs ph…
In gauge theories with an extended Higgs sector the classical equations of motion can have solutions that describe stable, closed finite energy vortices. Such vortices separate two disjoint Higgs vacua, with one of the vacua embedded in the other in a manner that forms a topologically nontrivial knot. The knottedness stabilizes the vortex against shrinkage in 3+1 dimensional space-time. But in a world with extra large dimensions we expect the configuration to decay by unknotting. As an example we consider the semilocal $θ_W \to \fracπ{2}$ limit of the Weinberg-Salam model. We present numerical…
We show that there is a constraint on the parameter space of two Higgs doublet models that comes from the existence of the stable vortex-domain wall systems. The constraint is quite universal in the sense that it depends on only two combinations of Lagrangian parameters and does not depend on how fermions couple to two Higgs fields. Numerical solutions of field configurations of domain wall-vortex system are obtained, which provide a basis for further quantitative study of cosmology which involve such topological objects.
A numerical search for bosonic superconducting static vortex rings in a $U(1)_{A}\times U(1)_{W}$ model is presented. The fate of these rings without current, is to shrink due to their tension until extinction. The superconductivity of the loop does not seem to prevent shrinking. Current quenching takes place before stabilization.
Embedded defects proposed long ago (Z-vortices and Nambu monopoles) have been successfully searched for in 3D equilibrium lattice studies within the standard model near the electroweak phase transition and the crossover (which follows it for realistic Higgs mass). Gauge independent lattice-vortex operators are proposed. Vortex condensation (percolation) is found to characterize the high-temperature phase. Small vortex clusters are thermally activated with non-negligible density on the low-temperature side only at higher Higgs mass, where preliminary evidence supports their semiclassical nature…
Vortex solutions in the two Higgs doublet electroweak model are constructed, and their stability to small perturbations is studied. The most general perturbation is decomposed into angular momentum modes, the least stable mode is identified, and the linearised energy change of the vortex under this perturbation is calculated numerically for various choices of parameters, thus determining whether or not the string is stable. It is found that, for realistic values of the Higgs mass and Weinberg angle, the string is unstable.
We show analytically and numerically the existence of double vortex solutions in two-Higgs systems. These solutions are generalizations of the \no vortices and exist for all values of the parameters in the Lagrangians considered. We derive analytically the asymptotic behavior of the solutions and confirm it numerically by solving the field equations. Finally, we show that these solutions can be embedded in realistic theories like the two-doublet extension of the standard model.
