Electroweak Strings Research Articles

Electroweak strings in the standard model

We argue that the existence of the electroweak monopole predicts the existence of the electroweak string in the standard model made of monopole–antimonopole pair separated infinitely apart, which carry the quantized magnetic flux 4πn/e\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4 \\pi n/e$$\\end{document}. We show how to construct such quantized magnetic flux string solution. Our result strongly indicates that genuine fundamental electromagnetic string could exist in nature which could actually be detected. We discuss the physical implications of our result in cosmology.

Neutrino zeromodes on electroweak strings in light of topological insulators

We examine neutrino zeromode solutions on the electroweak Z-string and their effect on the stability of the string in the standard model and its extensions. We propose using topological invariants constructed from the momentum (and real) space topology of Green’s functions, often used for investigating edge modes in condensed matter physics. We analyze the standard model and then examine type-I and type-II extensions of the neutrino sector as well as their hybrid. Based on this analysis, we also comment on proposals in the literature to stabilize the Z-string.

Stability of nontopological string in supersymmetric SU(2)×U(1) gauge theory

We construct a nontopological string solution for a supersymmetric gauge theory with [Formula: see text] gauge symmetry which is spontaneously broken to [Formula: see text] by developing the vacuum expectation value of two doublet Higgses. It is a supersymmetric extension of the electroweak string while supersymmetry is unbroken. We discuss the classical stability of the nontopological string by perturbations. We show that the classical stability is determined only by two parameters, and that the allowed region becomes essentially the same as in the electroweak string.

Quantum corrections to soliton energies

We review recent progress in the computation of leading quantum corrections to the energies of classical solitons with topological structure, including multi-soliton models in one space dimension and string configurations in three space dimensions. Taking advantage of analytic continuation techniques to efficiently organize the calculations, we show how quantum corrections affect the stability of solitons in the Shifman–Voloshin model, stabilize charged electroweak strings coupled to a heavy fermion doublet, and bind Nielsen–Olesen vortices at the classical transition between type I and type II superconductors.

Kibble mechanism for electroweak magnetic monopoles and magnetic fields

The vacuum manifold of the standard electroweak model is a three-sphere when one considers homogeneous Higgs field configurations. For inhomogeneous configurations we argue that the vacuum manifold is the Hopf fibered three sphere and that this viewpoint leads to general criteria to detect electroweak monopoles and Z-strings. We extend the Kibble mechanism to study the formation of electroweak monopoles and strings during electroweak symmetry breaking. The distribution of magnetic monopoles produces magnetic fields that have a spectrum Bλ ∝ λ−2, where λ is a smearing length scale. Even as the magnetic monopoles annihilate due to the confining Z-strings, the magnetic field evolves with the turbulent plasma and may be relevant for cosmological observations.

Electroweak axion string and superconductivity

We study the axion strings with the electroweak gauge flux in the DFSZ axion model and show that these strings, called the electroweak axion strings, can exhibit superconductivity without fermionic zeromodes. We construct three types of electroweak axion string solutions. Among them, the string with W-flux can be lightest in some parameter space, which leads to a stable superconducting cosmic string. We also show that a large electric current can flow along the string due to the Peccei-Quinn scale much higher than the electroweak scale. This large current induces a net attractive force between the axion strings with the same topological charge, which opens a novel possibility that the axion strings form Y-junctions in the early universe.

Electroweak strings with dark scalar condensates and their stability

The stability of "visible" electroweak-type cosmic strings is investigated in an extension of the Standard Model (SM) by a minimal dark sector, consisting of a U(1) gauge field, broken spontaneously by a scalar. The "visible" and dark sectors are coupled through a Higgs-portal and a gauge-kinetic mixing term. It is found that strings whose core is "filled" with a dark scalar condensate exhibit better stability properties than their analogues in the SM, when the electroweak mixing angle is close to $\theta_{\rm W}=\pi/2$. They become unstable as one lets $\theta_{\rm W}$ approach its physical value. The instability mechanism appears to be a $W$-boson condensation mechanism found in previous studies on the stability of electroweak strings.

Topology of electroweak vacua

In the Standard Model, the electroweak symmetry is broken by a complex, SU(2)-doublet Higgs field and the vacuum manifold SU(2)×U(1)/U(1) has the topology of a 3-sphere. We remark that there exist theoretical alternatives that are locally isomorphic, but in which the vacuum manifold is homeomorphic to an arbitrary non-trivial principal U(1)-bundle over a 2-sphere. These alternatives have non-trivial fundamental group and thus feature topologically-stable electroweak strings. An alternative based on the manifold RP3 (with fundamental group Z/2) allows custodial protection of gauge boson masses and their couplings to fermions and has an explicit realisation in the Minimal Composite Higgs Model, in the case of maximal electroweak symmetry breaking. We show that, in common with all alternatives to S3, such models have a problem with fermion masses.

Stabilization of semilocal strings by dark scalar condensates

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.

Brane realization of Nambu monopoles and electroweak strings

In the standard model, the electroweak Z-string can end on a Nambu monopole, whose mass is calculated to be 689 GeV from the current precise experimental data assuming the new particle with mass 125 GeV to be the Higgs boson. We study an extension of the standard model with additional singlet and triplet Higgs fields in the framework of N=1 supersymmetric field theory by using a D-brane configuration in type IIA string theory. We construct a D-brane configuration describing the electroweak symmetry breaking, and find a single D2-brane configuration describing a Z-string and a Nambu monopole attached by a Z-string in the standard model without an adjoint Higgs field. We further find a single D2-brane configuration describing a composite of a 't Hooft-Polyakov monopole and a Nambu monopole attached by a Z-string in an extended standard model with an adjoint Higgs field. We compute the binding energy of the 't Hooft-Polyakov and Nambu monopoles by solving a minimal surface area of a D2-brane.

Can Primordial Magnetic Fields Seeded by Electroweak Strings Cause an Alignment of Quasar Axes on Cosmological Scales?

The decay of nontopological electroweak strings may leave an observable imprint in the Universe today in the form of primordial magnetic fields. Protogalaxies preferentially tend to form with their axis of rotation parallel to an external magnetic field, and, moreover, an external magnetic field produces torque which tends to align the galaxy axis with the magnetic field. We demonstrate that the shape of a magnetic field left over from two looped electroweak strings can explain the observed nontrivial alignment of quasar polarization vectors and make predictions for future observations.

Yoichiro Nambu: Seer of modern physics

In this article I try to explain, in as non-mathematical a manner as possible, the path-breaking contributions of Yoichiro Nambu who was awarded the Nobel Prize in Physics for 2008. It can easily be said that the three pillars of modern high energy physics are: The Electroweak Theory, Quantum Chromodynamics and String Theory. Nambu made fundamental contributions in all these areas.

COSMOLOGICAL DEFECT AND HIGH ENERGY EXPERIMENTS

The production and evolution of cosmological defects are investigated based on the standard particle physics theory such as the electroweak unified model and quantum chromodynamics. In these models, the string type solution can be obtained. Although electroweak strings and pion strings are embedded ones and topologically unstable, they would be stabilized by high temperature plasma and bring various cosmological consequences. Moreover, the production of pion strings may be observed in the LHC experiment.

Finite temperature corrections and embedded strings in noncommutative geometry and the standard model with neutrino mixing

The recent extension of the standard model to include massive neutrinos in the framework of noncommutative geometry and the spectral action principle involves new scalar fields and their interactions with the usual complex scalar doublet. After ensuring that they bring no unphysical consequences, we address the question of how these fields affect the physics predicted in the Weinberg-Salam theory, particularly in the context of the electroweak phase transition. Applying the Dolan-Jackiw procedure, we calculate the finite temperature corrections, and find that the phase transition is first order. The new scalar interactions significantly improve the stability of the electroweak Z string, through the “bag” phenomenon described by Vachaspati and Watkins [“Bound states can stabilize electroweak strings,” Phys. Lett. B 318, 163–168 (1993)]. (Recently, cosmic strings have climbed back into interest due to a new evidence.) Sourced by static embedded strings, an internal space analogy of Cartan’s torsion is drawn, and a possible Higgs-force-like “gravitational” effect of this nonpropagating torsion on the fermion masses is described. We also check that the field generating the Majorana mass for the νR is nonzero in the physical vacuum.

Superconducting electroweak strings

Classical solutions describing strings endowed with an electric charge and carrying a constant electromagnetic current are constructed within the bosonic sector of the electroweak theory. For any given ratio of the Higgs boson mass to W boson mass and for any Weinberg's angle, these strings comprise a family that can be parameterized by values of the current through their cross section, I 3 , by their electric charge per unit string length, I 0 , and by two integers. These parameters determine the electromagnetic and Z fluxes, as well as the angular momentum and momentum densities of the string. For I 0 → 0 and I 3 → 0 the solutions reduce to Z strings, or, for solutions with I 0 = ± I 3 , to the W-dressed Z strings whose existence was discussed some time ago.

The evolution and persistence of dumbbells

We use large-scale numerical simulations to study the formation and evolution of non-topological defects in a generalized electroweak phase transition described by the Glashow-Salam-Weinberg model without fermions. Such defects include dumbbells, comprising a pair of monopoles joined by a segment of electroweak string. These exhibit complex dynamics, with some shrinking under the string tension and others growing due to the monopole-antimonopole attractions between near neighbours. We estimate the range of parameters where the network of dumbbells persists, and show that this region is narrower than the region within which infinite straight electroweak strings are perturbatively stable.

Neutrino Zero Modes and Stability of Electroweak Strings

We discuss massive and massless neutrino zero modes on electroweak strings. We argue that the eventual absence of the neutrino zero mode implies the existence of topogically stable strings where the required non-trivial topology has been induced by the fermionic sector.

Mining energy from a black hole by strings

We discuss how cosmic strings can be used to mine energy from black holes. A string attached to the black hole gives rise to an additional channel for the energy release. It is demonstrated that when a string crosses the event horizon, its transverse degrees of freedom are thermally excited and thermal string perturbations propagate along the string to infinity. The internal metric induced on the 2D world sheet of the static string crossing the horizon describes a 2D black hole. For this reason thermal radiation of string excitations propagating along the string can be interpreted as Hawking radiation of the 2D black hole. It is shown that the rate of energy emission through the string channel is of the same order of magnitude as the bulk radiation of the black hole. Thus, for ${N}_{s}$ strings attached to the black hole the efficiency of string channels is increased by factor ${N}_{s}.$ We discuss restrictions on ${N}_{s}$ which exist because of the finite thickness of strings, the gravitational back reaction and quantum fluctuations. Our conclusion is that the energy emission rate by strings can be increased as compared to the standard emission in the bulk by the factor ${10}^{3}$ for GUT strings and up to the factor ${10}^{31}$ for electroweak strings.

The Dirac sea contribution to the energy of an electroweak string

We present a systematic determination of the order ℏ fermionic energy shift when an electroweak string is perturbed. We show that the combined effect of zero-modes, bound states and continuum states is to lower the total fermionic ground state energy of the string when the Higgs instability of the string is excited. The effect of the Dirac sea is thus to destabilise the string. However, this effect can be offset by populating positive energy states. Fermions enhance the stability of an electroweak string with sufficiently populated fermionic bound states.

Stability of string defects in models of non-Abelian symmetry breaking

In this paper we describe a new type of topological defect, called a homilia string, which is stabilized through interactions with the string network. Using analytical and numerical techniques, we investigate the stability and dynamics of homilia strings, and show that they are stable in the standard electroweak model. In $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}U(1)$ models of symmetry breaking the intersection of two homilia strings is identified with a non-axially symmetric sphaleron. Repulsive forces between the homilia strings causes them to separate, resulting in the annihilation of the sphaleron. Furthermore, it is shown that electroweak homilia string loops cannot stabilize as vortons, which circumvents the adverse cosmological problems associated with stable loops. The consequences for GUT scale homilia strings are also discussed.