Dimensional Abelian Higgs Model Research Articles

Negative radiation pressure in the abelian Higgs model

Interactions of small-amplitude monochromatic plane waves with domain walls in (1+1) dimensional abelian Higgs model with a sextic potential were studied. The effective force exerted on a domain wall was derived from a linearized equation and compared with numerical simulations of the original model. It was shown that the domain walls always accelerate in one direction, regardless of the direction of the incoming wave. This implies that in some cases an effect called negative radiation pressure is observed, i.e. instead of pushing, the wave pulls the soliton.

Spectral properties of the critical (1+1)-dimensional Abelian-Higgs model

Spectral properties of the critical (1+1)-dimensional Abelian-Higgs model

Comments on abelian Higgs models and persistent order

A natural question about Quantum Field Theory is whether there is a deformation to a trivial gapped phase. If the underlying theory has an anomaly, then symmetric deformations can never lead to a trivial phase. We discuss such discrete anomalies in Abelian Higgs models in 1+1 and 2+1 dimensions. We emphasize the role of charge conjugation symmetry in these anomalies; for example, we obtain nontrivial constraints on the degrees of freedom that live on a domain wall in the VBS phase of the Abelian Higgs model in 2+1 dimensions. In addition, as a byproduct of our analysis, we show that in 1+1 dimensions the Abelian Higgs model is dual to the Ising model. We also study variations of the Abelian Higgs model in 1+1 and 2+1 dimensions where there is no dynamical particle of unit charge. These models have a center symmetry and additional discrete anomalies. In the absence of a dynamical unit charge particle, the Ising transition in the 1+1 dimensional Abelian Higgs model is removed. These models without a unit charge particle exhibit a remarkably persistent order: we prove that the system cannot be disordered by either quantum or thermal fluctuations. Equivalently, when these theories are studied on a circle, no matter how small or large the circle is, the ground state is non-trivial.

Acoustic black holes and universal aspects of area products

In this paper we derive acoustic metrics in the (3+1)-dimensional Abelian Higgs model with higher derivative terms. We have found acoustic metrics that are conformally related to the Reissner–Nordström and Kerr–Newman metrics. The universal aspects of area products which depend only on quantized quantities such as conserved electric charge and angular momentum are also addressed. We relate these areas with entanglement entropy of acoustic black holes in BEC systems. We also have shown there is an equivalence between microscopic descriptions of axisymmetric acoustic black hole entropy in a BEC system in four and two dimensions. Particularly, the system seems to develop an analogue of the Kerr/CFT correspondence.

Рассеяние вихрей в абелевых моделях Хиггса на компактных римановых поверхностях

Абелевы модели Хиггса на римановых поверхностях являются естественным обобщением абелевой $(2+1)$-мерной модели Хиггса на плоскости, возникающей в теории сверхпроводимости. В модели на плоскости ранее было доказано, что при «медленном» движении двух вихрей (нулей поля Хиггса) после лобового столкновения они испытывают рассеяние под прямым углом, а при симметричном столкновении $N$ вихрей под равными углами происходит рассеяние на угол $\pi/N$. В критическом случае (при значении параметра модели, равном единице) этот результат можно получить с помощью так называемого адиабатического принципа, который утверждает, что динамические решения модели с малой кинетической энергией могут быть приближены геодезическими на пространстве модулей статических решений в метрике, задаваемой кинетической энергией (кинетической метрике). Адиабатический принцип в абелевой $(2+1)$-мерной модели Хиггса в критическом случае был недавно строго обоснован. Хотя явный вид метрики не удается выписать даже в случае двух вихрей, наличие требуемых геодезических удается установить, пользуясь гладкостью метрики в координатах, задаваемых симметрическими функциями положений вихрей, и свойствами симметрии метрики. Локальный аналог этого результата можно доказать, пользуясь только гладкостью кинетической метрики. Это позволяет предположить, что локальный вариант утверждения о рассеянии $N$ вихрей на угол $\pi/N$ при симметричном столкновении переносится на случай моделей на римановых поверхностях. В работе показано, что наличие геодезических кинетической метрики, описывающих требуемое поведение вихрей, в моделях на компактных римановых поверхностях следует из гладкости кинетической метрики в симметрических координатах в окрестности точек столкновения всех вихрей. Указанное свойство гладкости доказано в случае компактных римановых поверхностей. Применив адиабатический принцип для моделей на римановых поверхностях, можно получить утверждение о локальном рассеянии медленно движущихся вихрей в динамических моделях на компактных римановых поверхностях. К сожалению, этот адиабатический принцип еще нуждается в строгом обосновании.

Quantum corrections to vortex masses and energies

We study the $2+1$ dimensional Abelian Higgs model defined on a spatial torus at critical self-coupling. We propose a method to compute the quantum contribution to the mass of the Abrikosov-Nielsen-Olesen vortex and to multivortex energies. The one-loop quantum correction to multivortex energies is computed analytically at the critical value of the torus area (Bradlow limit). For other values of the area one can set up an expansion around this critical area (Bradlow parameter expansion). The method is explained and the next-to-leading term explicitly evaluated. To this order, the resulting energies depend on the torus periods, but not on the vortex positions.

Phase transitions at strong coupling in the 2+1-d abelian Higgs model

We study, using numerical Monte-Carlo simulations, an effective description of the 2+1 dimensional Abelian Higgs model which is valid at strong coupling, in the broken symmetry sector. In this limit, the massive gauge boson and the massive neutral Higgs decouple leaving only the massive vortices. The vortices have no long range interactions. We find a phase transition as the mass of the vortices is made lighter and lighter. At the transition, the contributions to the functional integral come from a so-called infinite vortex anti-vortex loop. Adding the Chern-Simons term simply counts the linking number between the vortices. We find that the Wilson loop exhibits perimeter law behaviour in both phases, although the polarization cloud increases by an order of magnitude at the transition. We also study the 't Hooft loop. We find the 't Hooft loop exhibits perimeter law behaviour in the presence of the Chern-Simons term but is trivial in its absence. Thus we have a theory with perimeter law for both the Wilson loop and the 't Hooft loop, but contains no massless particles.

Supersonic velocities in noncommutative acoustic black holes

In this paper we derive Schwarzschild and Kerr - like noncommutative acoustic black hole metrics in the (3+1)-dimensional noncommutative Abelian Higgs model. We have found that the changing in the Hawking temperature T_H due to spacetime noncommutativity account for supersonic velocities and analogously may also account for superluminal particles in the general form (v-c)/c=\Delta T_H/8T_H. Assuming this form is also valid for gravitational black holes and particle physics, we have found that for \Delta T_H about the heaviest muon neutrino mass and T_H about proton mass gives 2.12\times 10-5 which agrees with the recent OPERA experiments. We also consider the Hawking temperature in terms of surface gravity to address the issue of background influence in the neutrino superluminality to show that our investigations also agree with supernova SN1987A measurements.

Phase transitions in a gas of anyons

We continue our numerical Monte Carlo simulation of a gas of closed loops on a 3 dimensional lattice, however, now in the presence of a topological term added to the action which corresponds to the total linking number between the loops. We compute the linking number using a novel approach employing certain notions from knot theory. Adding the topological term converts the particles into anyons. Interpreting the model as an effective theory that describes the $2+1$-dimensional Abelian Higgs model in the asymptotic strong-coupling regime, the topological linking number simply corresponds to the addition to the action of the Chern-Simons term. The system continues to exhibit a phase transition as a function of the vortex mass as it becomes small. We find the following new results. The Chern-Simons term has no effect on the Wilson loop. On the other hand, it does effect the 't Hooft loop of a given configuration, adding the linking number of the 't Hooft loop with all of the dynamical vortex loops. We find the unexpected result that both the Wilson loop and the 't Hooft loop exhibit a perimeter law even though there are no massless particles in the theory, in both phases of the theory. It should be noted that our method suffers from numerical instabilities if the coefficient of the Chern-Simons term is too large; thus, we have restricted our results to small values of this parameter. Furthermore, interpreting the lattice loop gas as an effective theory describing the Abelian Higgs model is only known to be true in the infinite coupling limit; for strong but finite coupling this correspondence is only a conjecture, the validity of which is beyond the scope of this article.

Acoustic black holes from Abelian Higgs model with Lorentz symmetry breaking

In this Letter we derive acoustic black hole metrics in the (3+1) and (2+1)-dimensional Abelian Higgs model with Lorentz symmetry breaking. In this set up the sound waves lose the Lorentz boost invariance and suffer a ‘birefringence’ effect. We have found acoustic black holes and respective Hawking temperatures depending on the Lorentz violating parameter. Furthermore, we obtain an acoustic Kerr-like black hole metric with the Lorentz violating term affecting its rate of loss of mass. We also have shown that for suitable values of the Lorentz violating parameter a wider spectrum of particle wave function can be scattered with increased amplitude by the acoustic black hole.

Phase transitions in a 3 dimensional lattice loop gas

We investigate, via Monte Carlo simulations, the phase structure of a system of closed, nonintersecting but otherwise non-interacting, loops in 3 Euclidean dimensions. The loops correspond to closed trajectories of massive particles and we find a phase transition as a function of their mass. We identify the order parameter as the average length of the loops at equilibrium. This order parameter exhibits a sharp increase as the mass is decreased through a critical value, the behaviour seems to be a cross-over transition. We believe that the model represents an effective description of the broken-symmetry sector of the 2+1 dimensional abelian Higgs model, in the extreme strong coupling limit. The massive gauge bosons and the neutral scalars are decoupled, and the relevant low-lying excitations correspond to vortices and anti-vortices. The functional integral can be approximated by a sum over simple, closed vortex loop configurations. We present a novel fashion to generate non-intersecting closed loops, starting from a tetrahedral tessellation of three space. The two phases that we find admit the following interpretation: the usual Higgs phase and a novel phase which is heralded by the appearance of effectively infinitely long loops. We compute the expectation value of the Wilson loop operator and that of the Polyakov loop operator. The Wilson loop exhibits perimeter law behaviour in both phases implying that the transition corresponds neither to the restoration of symmetry nor to confinement. The effective interaction between external charges is screened in both phases, however there is a dramatic increase in the polarization cloud in the novel phase as shown by the energy shift introduced by the Wilson loop.

Study of Dynamical Chiral Symmetry Breaking in (2 + 1) Dimensional Abelian Higgs Model

In this paper, we study the dynamical mass generation in the Abelian Higgs model in 2 + 1 dimensions. Instead of adopting the approximations in [Jiang H et al., J. Phys. A 41 2008 255402.], we numerically solve the coupled Dyson–Schwinger Equations (DSEs) for the fermion and gauge boson propagators using a specific truncation for the fermion-photon vertex ansatz and compare our results with the corresponding ones in the above mentioned paper. It is found that the results quoted in the above paper remain qualitatively unaffected by refining the truncation scheme of the DSEs, although there exist large quantitative differences between the results presented in the above paper and ours. In addition, our numerical results show that the critical number of fermion flavor Nc decreases steeply with the the gauge boson mass ma (or the ratio of the Higgs mass mh to the gauge boson mass ma, r = mh/ma) increasing. It is thus easier to generate a finite fermion mass by the mechanism of DCSB for a small ratio r for a given ma.

Can an odd number of fermions be created due to the chiral anomaly?

We describe a possible creation of an odd number of fractionally charged fermions in the 1+1 dimensional Abelian Higgs model. We point out that for 1+1 dimensions this process does not violate any symmetries of the theory, nor makes it mathematically inconsistent. We construct the proper definition of the fermionic determinant in this model and outline how to generalize it for calculation of preexponent in realistic mathematically consistent 3+1 dimensional models with the creation of an even number of fermions. © 2006 The American Physical Society.

Adiabatic paths and pseudoholomorphic curves

We consider the (2+1)-dimensional Abelian Higgs model, governed by the GinzburgLandau action functional and describe the adiabatic limit construction for this model. Then we switch to the 4-dimensional case and show that the Taubes correspondence may be considered as a (2+2)-dimensional analogue of the adiabatic limit construction.

Topological order and the deconfinement transition in the(2+1)-dimensional compact Abelian Higgs model

We study an Abelian compact gauge theory minimally coupled to bosonic matter with charge $q$, which may undergo a confinement-deconfinement transition in $2+1$ dimensions. The transition is analyzed using a nonlocal order parameter $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{W}$, which is related to large Wilson loops for fractional charges. We map the model to a dual representation with no gauge field but only a global $q$-state clock symmetry and show that $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{W}$ corresponds to the domain wall energy of that model. $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{W}$ is also directly connected to the concept of topological order. We exploit these facts in Monte Carlo simulations to study the detailed nature of the deconfinement transition.

Radion induced baryogenesis

Recent work in two brane Randall-Sundrum models has shown that the radion can drive parametric amplification of particles on the TeV brane leading to a stage of cosmology similar to preheating. We consider radion induced preheating as a mechanism for electroweak scale baryogenesis and estimate the baryon to entropy ratio for some regions of parameter space. We also predict an upper bound for the radion mass which makes this baryogenesis mechanism testable. Finally, we verify some assumptions with numerical calculations of the 1+1 dimensional Abelian Higgs model.

Effects of topology on the light front

We discuss how to construct theta vacua in the light-front field theories using the 1+1 dimensional Abelian Higgs model as an example. Unlike the non-gauged scalar field, zero modes of the Higgs field are in general dynamical as well as the gauge-field zero mode. While symmetry breaking is discussed in semi-classical treatment of the zero modes, the theta vacua are introduced in the quantum level by use of the large gauge symmetry.

QUANTUM MAGNETIC VORTICES AT FINITE TEMPERATURE IN (3 + 1)-D

We study the effect of a finite temperature on the correlation function of quantum magnetic vortex lines in the framework of the (3 + 1)-dimensional Abelian Higgs model. The vortex energy is inferred from the large distance behavior of these correlation functions. For large straight vortices of length L, we obtain that the energy is proportional to TL2 differently from the zero temperature result which is proportional to L. The case of closed strings is also analyzed. For T = 0, we evaluate the correlation function and energy of a large ring. Finite closed vortices do not exist as genuine excitations for any temperature.

High-temperature behavior of the Chern-Simons diffusion rate in the 1 + 1 dimensional abelian Higgs model

We give arguments that in the 1+1-dimensional abelian Higgs model the classical approximation can be good for the leading high-temperature behavior of real-time processes. The Chern-Simons diffusion rate (‘sphaleron rate’) is studied numerically in this approximation. New results at high-temperature show a T 2 3 behavior of the rate at sufficiently small lattice spacing.

Supergravity and a Bogomol'nyi bound in three dimensions

We discuss the (2 + 1)-dimensional Abelian Higgs model coupled to N = 2 supergravity. The model provides an example on how unbroken supercharges can be defined, circumventing the problem of finding supercovariantly constant Killing spinors in 2+1 dimensions. We show that this is due to the existence of gravitating vortices saturating a Bogomol'nyi bound. The corresponding self-duality equations imply, through an integrability condition, the Einstein equation.