Quantum fluctuations around low-dimensional topological solitons

2014

Eur. Phys. J. C

We show that Abelian Higgs Models with a 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) × U (1) semilocal model with a doublet of complex scalar fields. The variety of known noncommutative self-dual vortices which display a regular behavior when the noncommutativity parameter tends to zero results in this way considerably enlarged.

Section: Discussionmentioning

confidence: 99%

Section: Noncommutative Vortex Profilesmentioning

confidence: 99%

See 1 more Smart Citation

Self-dual vortices in Abelian Higgs models with dielectric function on the noncommutative plane

2014

Eur. Phys. J. C

“…The new method requires precise information about the zero mode wave functions such that the information gathered in this paper is necessary to improve the results obtained in [18][19][20][21][22] by diminishing the impact of zero modes in heat kernel expansions. 2 However, vortex zero modes exist and are influential not only in critical vortices between Type I and II superconductors.…”

Section: Jhep05(2016)074mentioning

confidence: 99%

Dissecting zero modes and bound states on BPS vortices in Ginzburg-Landau superconductors

Izquierdo

2016

J. High Energ. Phys.

In this paper the zero modes of fluctuation of cylindrically symmetric self-dual vortices are analyzed and described in full detail. These BPS topological defects arise at the critical point between Type II and Type I superconductors, or, equivalently, when the masses of the Higgs particle and the vector boson in the Abelian Higgs model are equal. In addition, novel bound states of Higss and vector bosons trapped by the self-dual vortices at their core are found and investigated.

“…references [45,46]. Moreover, the winding number of the map from the S 1 ∞ circle enclosing the spatial plane to the S 1 fiber provided by the gauge field at infinity classifies the configuration space in n ∈ Z disconnected subspaces.…”

Section: Jhep02(2015)139mentioning

confidence: 99%

Two species of vortices in massive gauged non-linear sigma models

Izquierdo

2015

J. High Energ. Phys.

Non-linear sigma models with scalar fields taking values on CP n complex manifolds are addressed. In the simplest n = 1 case, where the target manifold is the S 2 sphere, we describe the scalar fields by means of stereographic maps. In this case when the U(1) symmetry is gauged and Maxwell and mass terms are allowed, the model accommodates stable self-dual vortices of two kinds with different energies per unit length and where the Higgs field winds at the cores around the two opposite poles of the sphere. Allowing for dielectric functions in the magnetic field, similar and richer self-dual vortices of different species in the south and north charts can be found by slightly modifying the potential. Two different situations are envisaged: either the vacuum orbit lies on a parallel in the sphere, or one pole and the same parallel form the vacuum orbit. Besides the selfdual vortices of two species, there exist BPS domain walls in the second case. Replacing the Maxwell contribution of the gauge field to the action by the second Chern-Simons secondary class, only possible in (2 + 1)-dimensional Minkowski space-time, new BPS topological defects of two species appear. Namely, both BPS vortices and domain ribbons in the south and the north charts exist because the vacuum orbit consits of the two poles and one parallel. Formulation of the gauged CP 2 model in a reference chart shows a self-dual structure such that BPS semi-local vortices exist. The transition functions to the second or third charts break the U(1) × SU(2) semi-local symmetry, but there is still room for standard self-dual vortices of the second species. The same structures encompassing N complex scalar fields are easily generalized to gauged CP N models.