Selfgravitating electroweak strings

Chae, Dongho; Tarantello, Gabriella

doi:10.1016/j.jde.2004.10.008

Cited by 9 publications

(6 citation statements)

References 16 publications

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“…We also recall [49] and [36] for other interesting results about Liouville's systems. Concerning self-dual electroweak vortices, we mention the work in [120], [27] and [28] in the planar case, and [119], [11] in the periodic case where sharp existence results are established for vortex number N = 1, 2, 3, 4. The analysis of the case N > 4 is still incomplete and in this direction a first contribution is contained in [9] that aims to extend the analysis of [43], [44] to "singular" Liouville-type equations in presence of Dirac measures.…”

Section: Vol 72 (2004)mentioning

confidence: 99%

Selfdual Maxwell-Chern-Simons Vortices

Tarantello

2004

Milan j. math.

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Section: Vol 72 (2004)mentioning

confidence: 99%

Selfdual Maxwell-Chern-Simons Vortices

Tarantello

2004

Milan j. math.

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“…By the well known uniqueness and non degeneracy properties of solutions of (6.63), see [40], and the advanced "perturbation" techniques available in literature (see e.g. [8], [9], [15], [16], [27]and [26]) it should be possible to exhibit explicit examples of solution sequences of (2.18), (2.19) which satisfies (2.20) and whose blow-up behaviour is characterised by (2.27).…”

Section: )mentioning

confidence: 99%

Blow-up analysis for a cosmic strings equation

Tarantello

2017

Journal of Functional Analysis

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In this paper we develop a blow-up analysis for solutions of an elliptic PDE of Liouville type over the plane. Such solutions describe the behavior of cosmic strings (parallel in a given direction) for a W-boson model coupled with Einstein's equation. We show how the blow-up behavior of the solutions is characterized, according to the physical parameters involved, by new and surprising phenomena. For example in some cases, after a suitable scaling, the blow-up profile of the solution is described in terms of an equations that bares a geometrical meaning in the context of the "uniformization" of the Riemann sphere with conical singularities.

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“…In addition, we shall construct a first class of finite-energy (radial) solutions, which enjoy a physically interesting "concentration" property. To this end, we use a perturbation approach introduced in [9] to deal with Abelian non-topological Chern-Simons vortices, and further developed in [10,11] for self-dual electroweak models with and without gravitational effects. More precisely, we shall identify an appropriate new scaling for the solution, which, in one hand, sets our problem into a "perturbation" framework, and at the same time also helps to clarify its specific analytic features.…”

Section: Introductionmentioning

confidence: 99%

Non-topological Vortex Configurations in the ABJM Model

Han

Tarantello

2017

Commun. Math. Phys.

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In this paper we study the existence of vortex-type solutions for a system of self-dual equations deduced from the mass-deformed Aharony-Bergman-Jafferis-Maldacena (ABJM) model. The governing equations, derived by Mohammed, Murugan, and Nastse under suitable ansatz involving fuzzy sphere matrices, have the new feature that they can support only non-topological vortex solutions. After transforming the self-dual equations into a nonlinear elliptic 2 × 2 system we prove first an existence result by means of a perturbation argument based on a new and appropriate scaling for the solutions. Subsequently, we prove a more complete existence result by using a dynamical analysis together with a blow-up argument. In this way we establish that, any positive energy level is attained by a 1-parameter family of vortex solutions which also correspond to (constraint) energy minimizers. In other words, we register the exceptional fact in a BPS-setting that, neither a "quantization" effect nor an energy gap is induced upon the system by the rigid "critical" coupling of the self-dual regime.

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Selfgravitating electroweak strings

Cited by 9 publications

References 16 publications

Selfdual Maxwell-Chern-Simons Vortices

Selfdual Maxwell-Chern-Simons Vortices

Blow-up analysis for a cosmic strings equation

Non-topological Vortex Configurations in the ABJM Model

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