In this work there are proposed several new 6D brane worlds based on exact topological solutions to the vortex equations for the Abelian Higgs model, with suitable boundary conditions and symmetry breaking potentials similar to the mexican hat. Just as happens for RS domain wall brane worlds, it is shown that the massless mode of linearized gravity is localized in the neighborhood of the string-vortex solution while there are not massive bounded states. The correction to the newtonian limit of the effective 4D gravity is calculated.
We investigate the Non-Commutative Abelian Higgs model. We argue that it is possible to introduce a consistent renormalization method by imposing the Non-commutative BRST invariance of the theory and by introducing the Non-Commutative Quasi-Classical Action Principle.
Applying Cho-Faddeev-Niemi decomposition for SU(2) Yang-Mills field, we obtain the Abelian-Higgs Lagrangian by some approximation. Abelian-Higgs Lagrangian with a spontaneous symmetry breaking potential has vortex solutions known as Nielsen-Olesen solutions. We conclude that vortices as well as magnetic monopoles can exist in Cho-Faddeev-Niemi decomposition of SU(2) Yang-Mills field.
This work deals with several aspects of the extension to Abelian Higgs models of the deformation method originally developed for scalar field models. We present several examples allowing to transform self-dual solutions of different generalized Abelian Higgs models into scalar field models with or without a gauge field component. This is done through a parametrization of the soliton orbit in terms of the sine-Gordon static kink. We extend these ideas to a nonAbelian Higgs model.
The excitations of the vortex in Abelian Higgs model with small ratio of vector and Higgs particle masses are considered. Three main modes encountered in numerical computations are described in detail. They are also compared to analytic results obtained recently by Arodz and Hadasz.
We show that the Abelian Higgs field equations in the background of the four dimensional AdS-Schwarzschild black hole have a vortex line solution. This solution, which has axial symmetry, is a generalization of the AdS spacetime Nielsen-Olesen string. By a numerical study of the field equations, we show that black hole could support the Abelian Higgs field as its Abelian hair. Also, we conside the self gravity of the Abelian Higgs field both in the pure AdS spacetime and AdS-Schwarzschild black hole background and show that the effect of string as a black hole hair is to induce a deficit angle…
In this paper the two dimensional abelian Higgs model is revisited. We show that in the physical sector, the solutions to the Euler-Lagrange equations include solitons.
The four dimensional Abelian Higgs model with monopoles and $Θ$-term is considered in the limit of the large mass of the higgs boson. We show that for $Θ=2 π$ the theory is equivalent, at large distances, to summation over all possible world-sheets of fermionic strings with Dirichlet type boundary conditions on string coordinates.
It is shown that SU(2) QCD admits an dual Abelian-Higgs phase, with a Higgs vacuum type of type-II superconductor. This is done by using connection decomposition for the gluon field and the random-direction approximation. Using bag picture with soft wall, we presented a calculational procedure for glueball energy based on the recent proof for wall-vortices [Nucl. Phys. B 741(2006)1].
The N=2 supersymmetric extension of the 2+1 dimensional Abelian Higgs model is discussed. By analysing the resulting supercharge algebra, the connection between supersymmetry and Bogomol'nyi equations is clarified. Analogous results are presented when the model is considered in 2-dimensional (Euclidean) space.
We study the problem of vortex solutions in the background of an electrically charged black string. We show numerically that the Abelian Higgs field equations in the background of a four-dimensional black string have vortex solutions. These solutions which have axial symmetry, show that the black string can support the Abelian Higgs field as hair. This situation holds also in the case of the extremal black string. We also consider the self-gravity of the Abelian Higgs field and show that the effect of the vortex is to induce a deficit angle in the metric under consideration.
We show that the topological $B \wedge F$ term in $3+1$ dimensions can be generated via spontaneous symmetry breaking in a generalized Abelian Higgs model. Further, we also show that even in $D$ dimensions $ ( D \geq 3 ) $, a $B \wedge F$ term gives rise to the topological massive excitations of the Abelian gauge field and that such a $B \wedge F$ term can also be generated via Higgs mechanism.
We consider the classical equations of the gravitating Abelian-Higgs model in an axially symmetric ansatz. More properties of the solutions of these equations (the Melvin and the sting branches) are presented. These solutions are also constructed for winding numbers N=2. It is shown that these vortices exist in attractive and repulsive phases, separated by the value of the Higgs coupling constant parameter leading to self-dual equations.
We count Higgs "phase" BPS states of general non-Abelian quiver, possibly with loops, by mapping the problem to its Abelian, or toric, counterpart and imposing Weyl invariance later. Precise Higgs index computation is particularly important for quivers with superpotentials; the Coulomb "phase" index is recently shown to miss important BPS states, dubbed intrinsic Higgs states or quiver invariants. We demonstrate how the refined Higgs index is naturally decomposed to a sum over partitions of the charge. We conjecture, and show in simple cases, that this decomposition expresses the Higgs index a…
The low energy dynamics of the vortices of the Abelian Chern-Simons-Higgs system is investigated from the adiabatic approach. The difficulties involved in treating the field evolution as motion on the moduli space in this system are shown. Another two generalized Abelian Higgs systems are discusssed with respect to their vortex dynamics at the adiabatic limit. The method works well and we find bound states in the first model and scattering at right angles in the second system.
By making use of the duality transformation, gauge field correlators of the Abelian Higgs Model are studied in the London limit. The obtained results are in a good agreement with the dual Meissner scenario of confinement and with the Stochastic Model of QCD vacuum. The nontrivial contribution to the quartic correlator arising due to accounting for the finiteness of the coupling constant is discussed.
In this paper the two dimensional Abelian Higgs model is revisited. We show that in the physical sector, this model describes the coupling of the electric field to the radial part, in field space, of the complex scalar field.
We consider the noncommutative Abelian-Higgs theory and construct new types of exact multi-vortex solutions that solve the static equations of motion. They in general do not follow from the BPS equations; only for some specific values of parameters, they satisfy the BPS equations saturating the Bogomol'nyi bound. We further consider the Abelian-Higgs theory with more complicated scalar potential allowing unstable minima and construct exact solutions of noncommutative false vacuum bubble with integer magnetic flux. The classical stability of the solutions is discussed.
We numerically study string production by evolving classical Abelian-Higgs gauge field wavepackets. Initial conditions are constructed for the propagation of a single wavepacket and for the collision of two wavepackets. We identify regions of parameter space that lead to prompt production of strings from a single wavepacket. The collision of two sub-critical wavepackets can also lead to the production of strings in certain regions of parameter space.
Following our earlier investigations we examine the quantum-classical winding number transition in the Abelian-Higgs system. It is demonstrated that the sphaleron transition in this system is of the smooth second order type in the full range of parameter space. Comparison of the action of classical vortices with that of the sphaleron supports our finding.
Non Abelian vortices of a SU(2) Chern-Simons--Higgs theory in 2+1 dimensions are constructed numerically. They represent natural counterparts of the U(1) solutions considered by Hong, Kim and Pac, and, by Jackiw and Weinberg. The Abelian embeddings are identified, for all values of the Higgs selfinteraction strength $ν$, resulting in both attractive and repulsive phases. A detailed analysis of the properties of the solutions reveals the existence ofa number of unexpected features. For a certain range of the parameter $ν$, it is shown that the non Abelian vortices have lower energy than their t…
We investigate new aspects related to the abelian gauge-Higgs model with the addition of the Carroll-Field-Jackiw term. We focus on one-loop quantum corrections to the photon and Higgs sectors due to spontaneous breaking of gauge symmetry and show that new finite and definite Lorentz-breaking terms are induced. Specifically in the gauge sector, a CPT-even aether term is induced. Besides, aspects of the one-loop renormalization of the background vector dependent terms are discussed.
We consider both the Abelian Higgs model and the impact of a minimal length in the un-particle sector. It is shown that even if the Higgs field takes a non-vanishing v.e.v., gauge interaction keeps its long range character leading to an effective gauge symmetry restoration. The effect of a quantum gravity induced minimal length on a physical observable is then estimated by using a physically-based alternative to the usual Wilson loop approach. Interestingly, we obtain an ultraviolet finite interaction energy described by a confluent hyper-geometric function, which shows a remarkable richness o…
We show that Abelian Higgs Models with dielectric function defined on the noncommutative plane enjoy self-dual vorticial solutions. By choosing a particular form of the dielectric function, we provide a family of solutions whose Higgs and magnetic fields interpolate between the profiles of the noncommutative Nielsen-Olesen and Chern-Simons vortices. This is done both for the usual $U(1)$ model and for the $SU(2)\times U(1)$ semilocal model with a doublet of complex scalar fields. The variety of known noncommutative self-dual vortices which display a regular behaviour when the noncommutativity …
By taking into account the effect of the would be Chern-Simons term, we calculate the quantum correction to the Chern-Simons coefficient in supersymmetric Chern-Simons Higgs theories with matter fields in the fundamental representation of SU(n). Because of supersymmetry, the corrections in the symmetric and Higgs phases are identical. In particular, the correction is vanishing for N=3 supersymmetric Chern-Simons Higgs theories. The result should be quite general, and have important implication for the more interesting case when the Higgs is in the adjoint representation.
We consider the classical equations of the Born-Infeld-Abelian-Higgs model (with and without coupling to gravity) in an axially symmetric ansatz. A numerical analysis of the equations reveals that the (gravitating) Nielsen-Olesen vortices are smoothly deformed by the Born-Infeld interaction, characterized by a coupling constant $β^2$, and that these solutions cease to exist at a critical value of $β^2$. When the critical value is approached, the length of the magnetic field on the symmetry axis becomes infinite.
By making use of the path integral duality transformation, we derive the string representation for the partition function of an extended Dual Abelian Higgs Model containing gauge fields of external currents of electrically charged particles. By the same method, we obtain the corresponding representations for the generating functionals of gauge field and monopole current correlators. In the case of bilocal correlators, the obtained results are found to be in agreement with the dual Meissner scenario of confinement and with the Stochastic Model of the QCD vacuum.
In the Abelian Higgs model electric (and magnetic) fields of external charges (and currents) are screened by the scalar field. In this contribution, complementing recent investigations of Ishihara and Ogawa, we present a detailed investigation of charge screening using a perturbative approach with the charge strength as an expansion parameter. It is shown how perfect global and remarkably good local screening can be derived from Gauss' theorem, and the asymptotic form of the fields far from the sources. The perturbative results are shown to compare favourably to the numerical ones.
We study the properties of a single magnetic vortex and magnetic vortex lattices in a generalization of the Abelian Higgs model containing the simplest derivative interaction that preserves the $U(1)$ gauge symmetry of the original model. The paper is motivated by the study of finite isospin chiral perturbation theory in a uniform, external : since pions are Goldstone bosons of QCD (due to chiral symmetry breaking by the QCD vacuum), they interact through momentum dependent terms. We introduce a uniform external magnetic field and find the asymptotic properties of single vortex solutions and c…
We examine the dependence on all gauge parameters in the example of the Abelian Higgs model by applying a general algebraic method which roots in an extension of the usual Slavnov-Taylor identity. This method automatically yields all information about the gauge parameter dependence of Green functions and therefore especially allows to control the range of ``good'' normalization conditions. In this context we show that the physical on-shell normalization conditions are in complete agreement with the restrictions dictated by the enlarged Slavnov-Taylor identity and that the coupling can be fixed…
In this paper we study a system inspired on certain SUSY breaking models and on more recent Dark Matter scenarios. In our set-up, two Abelian gauge fields interact via an operator that mixes their kinetic terms. We find the extended Supersymmetric version of this system, that also generates a Higgs portal type of interaction. We obtain and study both analytically and numerically, the equations defining topologically stable string-like objects. We check our results using two different approaches. Various technical details are explicitly stated for the benefit of various readers.
Self-dual vortex solutions are studied in detail in the generalized abelian Higgs model with independent Chern-Simons interaction. For special choices of couplings, it reduces to a Maxwell-Higgs model with two scalar fields, a Chern-Simons-Higgs model with two scalar fields, or other new models. We investigate the properties of the static solutions and perform detailed numerical analyses. For the Chern-Simons-Higgs model with two scalar fields in an asymmetric phase, we prove the existence of multisoliton solutions which can be viewed as hybrids of Chern-Simons vortices and $CP^1$ lumps. We al…
We propose a geometrized Higgs mechanism based on the gravitational sector in the Connes-Lott formulation of the standard model, which has been constructed by Chamseddine, Fr$\ddot{o}$hlic and Grandjean. The point of our idea is that Higgs-like couplings depend on the local coordinates of the four-dimensional continuum,$M_4$. The localized couplings can be calculated by the Wilson loops of the $U(1)_{EM}$ gauge field and the connection, which is defined on $Z_2\times{M_4}$.
We have studied a modified Yang-Mills-Higgs system coupled to Einstein gravity. The modification of the Einstein-Hilbert action involves a direct coupling of the Higgs field to the scalar curvature. In this modified system we are able to write a Bogomol'nyi type condition in curved space and demonstrate that the positive static energy functional is bounded from below. We then investigate non-Abelian sperically symmetric static solutions in a similar fashion to the `t Hooft-Polyakov monopole. After reviewing previously studied monopole solutions of this type, we extend the formalism to included…
Aspects of screening and confinement are re-examined for a recently proposed compact Abelian Higgs model with a $θ$-term. Our discussion is accomplished using the gauge-invariant but path-dependent variables formalism, which is an alternative to the Wilson loop approach. We explicitly show that the static potential profile is the sum of an effective-Yukawa and a linear potential, leading to the confinement of static external charges. We point out the central rôle of the parameter measuring the stiffness of the vortex lines present in the model in both the Yukawa-like and the confining sectors …
We consider a generalization of the abelian Higgs model with a Chern-Simons term by modifying two terms of the usual Lagrangian. We multiply a dielectric function with the Maxwell kinetic energy term and incorporate nonminimal interaction by considering generalized covariant derivative. We show that for a particular choice of the dielectric function this model admits topological vortices satisfying Bogomol'nyi bound for which the magnetic flux is not quantized even though the energy is quantized. Furthermore, the vortex solution in each topological sector is infinitely degenerate.
We present an extension of the deformation method applied to self-dual solutions of generalized Abelian Higgs-Chern-Simons models. Starting from a model defined by a potential $V(| ϕ|)$ and a non-canonical kinetic term $ω(| ϕ|) | D_μϕ|^2$ whose analytical domain wall solutions are known, we show that this method allows to obtain an uncountable number of new analytical solutions of new models defined by other functions $\widetilde{V}$ and $\widetildeω$. We present some examples of deformation functions leading to new families of models and their associated analytic solutions.
We have studied the existence of self-dual effective compact and true compacton configurations in Abelian Higgs models with generalized dynamics. We have named of an effective compact solution the one whose profile behavior is very similar to the one of a compacton structure but still preserves a tail in its asymptotic decay. In particular we have investigate the electrically neutral configurations of the Maxwell-Higgs and Born-Infeld-Higgs models and the electrically charged ones of the Chern-Simons-Higgs and Maxwell-Chern-Simons-Higgs models. The generalization of the kinetic terms is perfor…
Massless matter fields and non-Abelian gauge fields are localized on domain walls in a (4+1)-dimensional $U(N)_c$ gauge theory with $SU(N)_{L}\times SU(N)_{R}\times U(1)_{A}$ flavor symmetry. We also introduce $SU(N)_{L+R}$ flavor gauge fields and a scalar-field-dependent gauge coupling, which provides massless non-Abelian gauge fields localized on the wall. We find a chiral Lagrangian interacting minimally with the non-Abelian gauge field together with nonlinear interactions of moduli fields as the (3+1)-dimensional effective field theory up to the second order of derivatives. Our result prov…
We explore the low-temperature behavior of the Abelian Higgs model in AdS_4, away from the probe limit in which back-reaction of matter fields on the metric can be neglected. Over a significant range of charges for the complex scalar, we observe a second order phase transition at finite temperature. The symmetry-breaking states are superconducting black holes. At least when the charge of the scalar is not too small, we observe at low temperatures the emergence of a domain wall structure characterized by a definite index of refraction. We also compute the conductivity as a function of frequency…
We search a canonical basis of Dirac's observables for the classical non-Abelian Higgs model with fermions in the case of a trivial SU(2) principal bundle with a complex doublet of Higgs fields and with the fermions in a given representation of SU(2). Since each one of the three Gauss law first class constraints can be solved either in the corresponding longitudinal electric field or in the corresponding Higgs momentum, we get a priori eight disjoint phases of solutions of the model. The only two phases with SU(2) covariance are the SU(2) phase with massless SU(2) fields and the Higgs phase wi…
We present a numerical investigation of the dynamics of symmetry breaking in both Abelian and non-Abelian $[S U (2)]$ Higgs models in three spatial dimensions. We find a class of time-dependent, long-lived nonperturbative field configurations within the range of parameters corresponding to type-1 superconductors, that is, with vector masses ($m_v$) larger than scalar masses ($m_s$). We argue that these emergent nontopological configurations are related to oscillons found previously in other contexts. For the Abelian-Higgs model, our lattice implementation allows us to map the range of paramete…
We search a canonical basis of Dirac's observables for the classical Abelian Higgs model with fermions in the case of a trivial U(1) principal bundle. The study of the Gauss law first class constraint shows that the model has two disjoint sectors of solutions associated with two physically different phases. In the electromagnetic phase, the electromagnetic field remains massless: after the determination of the Dirac's observables we get that both the reduced physical Hamiltonian and Lagrangian are nonlocal. In the Higgs phase, the electromagnetic field becomes massive and in terms of Dirac's o…
We correct two errors in our previous computation of one-loop corrections to the vortex string tension: (i) the contribution of the longitudinal and timelike modes of the gauge fields were forgotten and are included now; (ii) a trivial error in the numerical code has led to considerable errors in the subtracted integrals. We here present the corrected results.
The fluctuation determinant, the preexponential factor for the instanton transition, has been computed several years ago in the Abelian Higgs model, using a method based on integrating the Euclidean Green' function. A more elegant method for computing functional determinants, using the Gel'fand-Yaglom theorem, has been applied recently to a variety of systems. This method runs into difficulties if the background field has nontrivial topology, as is the case for the instanton in the Abelian Higgs model. A shift in thre effective centrifugal barriers makes the s-wave contribution infinite, an in…
Making use of the duality transformation, we construct string representation for the partition function of the London limit of Abelian Higgs Model with an additional axionic term. In the lowest order of perturbation theory, this term leads to the appearance in the resulting string effective action of a new threelocal interaction between the elements of the string world-sheet. Consequently, there emerges a threelocal correlator of the dual field strength tensors, which does not contain the average over world-sheets, and is therefore nontrivial even in the sector of the theory with a single smal…
Starting from the Abelian Higgs field theory, we construct the theory of quantum Abrikosov--Nielsen--Olesen strings. It is shown that in four space -- time dimensions in the limit of infinitely thin strings, the conformal anomaly is absent, and the quantum theory exists. We also study an analogue of the Aharonov--Bohm effect: the corresponding topological interaction is proportional to the linking number of the string world sheet and the particle world trajectory. The creation operators of the strings are explicitly constructed in the path integral and in the Hamiltonian formulation of the the…
We calculate the one loop corrections to the Chern-Simons coefficient $κ$ in the Higgs phase of Yang-Mills Chern-Simons Higgs theories. When the gauge group is SU(N), we show, by taking into account the effect of the would be Chern-Simons term, that the corrections are always integer multiples of ${1\over 4π}$, as they should for the theories to be quantum-mechanically consistent. In particular, the correction is vanishing for SU(2). The same method can also be applied to the case that the gauge group is SO(N). The result for SO(2) agrees with that found in the abelian Chern-Simons theories. T…
Motivated by the study of holographic superconductors, we generalize no-hair theorems for minimally coupled scalar fields charged under an Abelian gauge field, in arbitrary dimensions and with arbitrary horizon topology. We first present a straightforward generalization of no-hair theorems for neutral scalar hair. We then consider the existence of extremal black holes with scalar hair, and in the case of horizons with zero or positive curvature, provide a bound on the mass and charge of the scalar field that are necessary for the scalar hair to develop.
A particular solution to the equations of motion of the Abelian Higgs model is given. The solution involves the Jacobi elliptic functions as well as the Heun functions.
We find 3-brane Higgs and Coulomb phases in the 5D Abelian Higgs Model and determine the transition surfaces that separate them from the usual bulk phases.
We examine the claim of Chamblin et. al. that extreme black holes cannot support abelian Higgs hair. We provide evidence that contradicts this claim and discuss reasons for this discrepancy.
Inspired by magnetic impurity considerations some broad classes of Abelian Higgs and Chern--Simons--Higgs BPS vortex equations are derived and analyzed.
The abelian Higgs model and its phase structure are discussed from the perspective that the gauge and scalar fields admit a dual description in terms of fermion variables. The results which indicate the presence of three main phases: Coulomb, Higgs and confinement agree well with those in the literature although a nonstandard order parameter is employed.
Motivated by the Higgs Inflation scenario, we study static spherically-symmetric solutions of the non-Abelian Higgs model coupled non-minimally to Gravity. We find solutions for the self-gravitating sphaleron as well as monopole-like solutions and study the impact of the non-minimal coupling on their properties. Finally we discuss shortly the possibility that these solutions interact gravitationally with star-like objects like boson stars.
We present an alternative to the Higgs mechanism to generate masses for non-abelian gauge fields in (3+1)-dimensions. The initial Lagrangian is composed of a fermion with current-current and dipole-dipole type self-interactions minimally coupled to non-abelian gauge fields. The mass generation occurs upon the fermionic functional integration. We show that by fine-tuning the coupling constants the effective theory contains massive non-abelian gauge fields without any residual scalars or other degrees of freedom.
We establish the phase diagram of the five-dimensional anisotropic Abelian Higgs model by mean field techniques and Monte Carlo simulations. The anisotropy is encoded in the gauge couplings as well as in the Higgs couplings. In addition to the usual bulk phases (confining, Coulomb and Higgs) we find four-dimensional ``layered'' phases (3-branes) at weak gauge coupling, where the layers may be in either the Coulomb or the Higgs phase, while the transverse directions are confining.
