We revisit previously developed analytic models for defect evolution and adapt them appropriately for the study of semilocal string networks. We thus confirm the expectation (based on numerical simulations) that linear scaling evolution is the attractor solution for a broad range of model parameters. We discuss in detail the evolution of individual semilocal segments, focusing on the phenomenology of segment growth, and also provide a preliminary comparison with existing numerical simulations.
In this work we calibrate two different analytic models of semilocal strings by constraining the values of their free parameters. In order to do so, we use data obtained from the largest and most accurate field theory simulations of semilocal strings to date, and compare several key properties with the predictions of the models. As this is still work in progress, we present some preliminary results together with descriptions of the methodology we are using in the characterisation of semilocal string networks.
Dark strings have recently been suggested to exist in new models of dark matter that explain the excessive electronic production in the galaxy. We study the interaction of these dark strings with semilocal strings which are solutions of the bosonic sector of the Standard Model in the limit $\sin^2θ_{\rm w}=1$, where $θ_{\rm w}$ is the Weinberg angle. While embedded Abelian-Higgs strings exist for generic values of the coupling constants, we show that semilocal solutions with non-vanishing condensate inside the string core exist only above a critical value of the Higgs to gauge boson mass ratio…
Semilocal and electroweak strings are well-known to be unstable against unwinding by the condensation of the second Higgs component in their cores. A large class of current models of dark matter contains dark scalar fields coupled to the Higgs sector of the Standard Model (Higgs portal) and/or dark U(1) gauge fields. It is shown, that Higgs-portal-type couplings and a gauge kinetic mixing term of the dark U(1) gauge field have a significant stabilising effect on semilocal strings in the "visible" sector.
Semilocal strings -- a particular limit of electroweak strings -- are an interesting example of a stable non-topological defect whose properties resemble those of their topological cousins, the Abrikosov-Nielsen-Olesen vortices. There is, however, one important difference: a network of semilocal strings will contain segments. These are 'dumbbells' whose ends behave almost like global monopoles that are strongly attracted to one another. While closed loops of string will eventually shrink and disappear, the segments can either shrink or grow, and a cosmological network of semilocal strings will…
It has been pointed out that cosmic string solutions can exist in gauge field theories with broken symmetry even when $π_1(G/H)$ is trivial. The stability of such semilocal defects is not guaranteed by topology and depends on dynamical considerations. In the literature it has been tacitly assumed that if stable, such strings would form in the Early Universe in a manner analogous to the formation of a network of more robust topologically-stable strings. In this paper we find that except for unnaturally small values of the correlation length, a network of semilocal strings does not form. Instead…
We continue a comprehensive numerical study of semilocal string networks and their cosmological evolution. These can be thought of as hybrid networks comprised of (non-topological) string segments, whose core structure is similar to that of Abelian Higgs vortices, and whose ends have long--range interactions and behaviour similar to that of global monopoles. Our study provides further evidence of a linear scaling regime, already reported in previous studies, for the typical length scale and velocity of the network. We introduce a new algorithm to identify the position of the segment cores. Thi…
We study the intercommuting of semilocal strings and Skyrmions, for a wide range of internal parameters, velocities and intersection angles by numerically evolving the equations of motion. We find that the collisions of strings and strings, strings and Skyrmions, and Skyrmions and Skyrmions, all lead to intercommuting for a wide range of parameters. Even the collisions of unstable Skyrmions and strings leads to intercommuting, demonstrating that the phenomenon of intercommuting is very robust, extending to dissimilar field configurations that are not stationary solutions. Even more remarkably,…
We report on a large scale numerical study of networks of semilocal cosmic strings in flat space in the parameter regime in which they are perturbatively stable. We find a population of segments with an exponential length distribution and indications of a scaling network without significant loop formation. Very deep in the stability regime strings of superhorizon size grow rapidly and ``percolate'' through the box. We believe these should lead at late times to a population of infinite strings similar to topologically stable strings. However, the strings are very light; scalar gradients dominat…
We report on a detailed numerical study of the evolution of semilocal string networks, based on the largest and most accurate field theory simulations of these objects to date. We focus on the large-scale network properties, confirming earlier indications (coming from smaller simulations) that linear scaling is the attractor solution for the entire parameter space of initial conditions that we are able to probe. We also provide a brief comparison of our numerical results with the predictions of a previously developed one-scale model for the overall evolution of these networks. Two subsequent p…
We demonstrate that the stability of the semilocal vortex can be significantly improved by the presence of a dilatonic coupling of the form e^\frac{q | Φ|^2}{η^2} F_{μν}F^{μν} with q>0 where ηis the scale of symmetry breaking that gives rise to the vortex. For q=0 we obtain the usual embedded (semilocal) Nielsen-Olesen vortex. We find the stability region of the parameter β= (\frac{m_Φ}{m_A})^2 (m_Φand m_A are the masses of the scalar and gauge fields respectively). We show that the stability region of βis 0<β<β_{max}(q) where β_{max}(q=0)=1 (as expected) and β_{max}(q) is an increasing functi…
We carry out three-dimensional numerical simulations to investigate the formation rate of semilocal strings. We find that the back-reaction of the gauge fields on the scalar field evolution is substantial, and leads to a significant formation rate in the parameter regime where the semilocal strings are classically stable. The formation rate can be as large as a third of that for cosmic strings, depending on the model parameters.
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. …
We review a class of non-topological defects in the standard electroweak model, and their implications. Starting with the semilocal string, which provides a counterexample to many well known properties of topological vortices, we discuss electroweak strings and their stability with and without external influences such as magnetic fields. Other known properties of electroweak strings and monopoles are described in some detail and their potential relevance to future particle accelerator experiments and to baryon number violating processes is considered. We also review recent progress on the cosm…
We study the stability properties of the twisted vortex solutions in the semilocal Abelian Higgs model with a global $\mathbf{SU}(2)$ invariance. This model can be viewed as the Weinberg-Salam theory in the limit where the non-Abelian gauge field decouples, or as a two component Ginzburg-Landau theory. The twisted vortices are characterized by a constant global current ${\cal I}$, and for ${\cal I}\to 0$ they reduce to the semilocal strings, that is to the Abrikosov-Nielsen-Olesen vortices embedded into the semilocal model. Solutions with ${\cal I}\neq 0$ are more complex and, in particular, t…
Among the inflationary models based on string theory, the D3/D7 model has the advantage that the flatness of the inflaton potential can be protected even with moduli stabilization. However, the Abrikosov-Nielsen-Olesen BPS cosmic strings produced at the end of original D3/D7 inflation lead to an additional contribution to the CMB anisotropy. To make this contribution consistent with the WMAP results one needs an extremely small gauge coupling in the effective D-term inflation model. Such couplings may be difficult to justify in string theory. Here we develop a generalized version of the D3/D7 …
We present a toy model for the investigation of the formation of semilocal strings, where a planar symmetry is employed to reduce the system to two dimensions. We approximate the symmetry breaking using an extension of the Vachaspati-Vilenkin algorithm, where we throw down random phases for the scalar fields and then find the gauge field configuration which minimizes gradient energy in this fixed scalar background. We show this procedure reproduces the standard estimate for the formation rate of cosmic strings. For semilocal strings the configurations generated by this method are ambiguous, an…
A new class of twisted, current carrying, stationary, straight string solutions having finite energy per unit length is constructed numerically in an extended Abelian Higgs model with global SU(2) symmetry. The new solutions correspond to deformations of the embedded Abrikosov-Nielsen-Olesen (ANO) vortices by a twist -- a relative coordinate dependent phase between the two Higgs fields. The twist induces a global current flowing through the string, and the deformed solutions bifurcate with the ANO vortices in the limit of vanishing current. For each value of the winding number $n=1,2...$ (dete…
We review recent simulations of the formation of a particular class of non-topological defects known as semilocal strings during a phase transition. Semilocal strings have properties that are intermediate between topological cosmic strings and stable electroweak strings, and therefore the observation that they could form in substantial quantities during a cosmological phase transition has implications for structure formation, baryogenesis, etc. At the same time, and from a purely theoretical point of view, they provide a very good testing ground for investigating the role of gauge fields in de…
I use a combination of state-of-the-art numerical simulations and analytic modelling to discuss the scaling properties of cosmic defect networks, including superstrings. Particular attention is given to the role of extra degrees of freedom in the evolution of these networks. Compared to the 'plain vanilla' case of Goto-Nambu strings, three such extensions play important but distinct roles in the network dynamics: the presence of charges/currents on the string worldsheet, the existence of junctions, and the possibility of a hierarchy of string tensions. I also comment on insights gained from st…
A linear stability analysis of twisted flux-tubes (strings) in an SU(2) semilocal theory -- an Abelian-Higgs model with two charged scalar fields with a global SU(2) symmetry -- is carried out. Here the twist refers to a relative phase between the two complex scalars (with linear dependence on, say, the $z$ coordinate), and importantly it leads to a global current flowing along the the string. Such twisted strings bifurcate with the Abrikosov-Nielsen-Olesen (ANO) solution embedded in the semilocal theory. Our numerical investigations of the small fluctuation spectrum confirm previous results t…
We show that local/semilocal strings in Abelian/non-Abelian gauge theories with critical couplings always reconnect classically in collision, by using moduli space approximation. The moduli matrix formalism explicitly identifies a well-defined set of the vortex moduli parameters. Our analysis of generic geodesic motion in terms of those shows right-angle scattering in head-on collision of two vortices, which is known to give the reconnection of the strings.
Nambu-Goldstone emissions from the cosmological evolution of global monopoles
Institute for Cosmic Ray Research, The University of Tokyo（宇宙线研究所，东京大学）；Frontier Research Institute for Interdisciplinary Sciences, Tohoku University（跨学科前沿科学研究所，东北大学）；Department of Physics, Tohoku University（物理学系，东北大学）
We derive analytic expressions for the interaction energy between two general $U(1)$ cosmic strings as the function of their relative orientation and the ratio of the coupling constants in the model. The results are relevant to the statistic description of strings away from critical coupling and shed some light on the mechanisms involved in string formation and the evolution of string networks.
We present a new generalized string model for Regge trajectories J=J(E^2), where J and E are the orbital momentum and energy of the string, respectively. We demonstrate that this model is not to produce linear Regge trajectories, in contrast to the standard Nambu-Goto string, but generally nonlinear trajectories, which in many cases can be given in analytic form. As an example, we show how the model generates square-root, logarithmic and hyperbolic trajectories that have been discussed in the literature.
We perform an analytic semi-classical quantization of the straight QCD string with one end fixed and a massless quark on the other, in the limits of orbital and radial dominant motion. We compare our results to the exact numerical semi-classical quantization. We observe that the numerical semi-classical quantization agrees well with our exact numerical canonical quantization.
We implement adaptive mesh refinement (AMR) simulations of global topological strings using the public numerical relativity code, GRChombo. We perform a quantitative investigation of the dynamics of single sinusoidally displaced string configurations, studying a wide range of string energy densities $μ\propto \lnλ$, defined by the string width parameter $λ$ over two orders of magnitude. We investigate the resulting massless (Goldstone boson or axion) radiation signals, using quantitative diagnostic tools to determine the eigenmode decomposition. Given analytic radiation predictions, we compare…
The properties of string networks at scales well below the horizon are poorly understood, but they enter critically into many observables. We argue that in some regimes, stretching will be the only relevant process governing the evolution. In this case, the string two-point function is determined up to normalization: the fractal dimension approaches one at short distance, but the rate of approach is characterized by an exponent that plays an essential role in network properties. The smoothness at short distance implies, for example, that cosmic string lensing images are little distorted. We th…
The evolution of cosmic string networks is an interesting dynamical problem. The equations governing these networks are classical and fully specified, but the length scale at which cosmic string loops form has been uncertain to tens of orders of magnitude. Numerical simulations are limited in the range of length and time scales they can reach, while analytic methods have been limited by the nonlinearities of the problem. We describe a recent analytic scaling model developed in collaboration with Jorge Rocha and Florian Dubath which, together with recent simulations, appears to resolve this que…
