Exploring the vicinity of the Bogomol'nyi-Prasad-Sommerfield bound

Almeida, Cristiane Maria Galdino de; Bazeia, D.; Losano, L.

doi:10.1088/0305-4470/34/16/302

Cited by 11 publications

(15 citation statements)

References 22 publications

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“…This feature is of direct interest to investigations that follow the lines of Ref. [54], which explores the vicinity of the BPS bound, and also in the case concerning the presence of internal modes of solitary waves, which seems to appear when one slightly modifies integrable modelssee for instance Ref. [55].…”

Section: B Single Field Two Kink Solutionsmentioning

confidence: 84%

Defect structures in sine-Gordon like models

Bazeia¹,

Losano²,

Menezes³

2005

Physica D: Nonlinear Phenomena

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We investigate several models described by real scalar fields, searching for topological defects. Some models are described by a single field, and support one or two topological sectors, and others are two-field models, which support several topological sectors. Almost all the defect structures that we find are stable and finite energy solutions of first-order differential equations that solve the corresponding equations of motion. In particular, for the double sine-Gordon model we show how to find small and large BPS solutions as deformations of the BPS solution of the φ 4 model. And also, for most of the two field models we find the corresponding integrating factors, which lead to the complete set of BPS solutions, nicely unveiling how they bifurcate among the several topological sectors.

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Section: B Single Field Two Kink Solutionsmentioning

confidence: 84%

Defect structures in sine-Gordon like models

Bazeia¹,

Losano²,

Menezes³

2005

Physica D: Nonlinear Phenomena

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“…for a real-valued generating function W [3,4,8,9,10,25], commonly referred to as the superpotential in the supersymmetric field theory formalism [4,11,22,23], to be specified later. The Euler-Lagrange equations of (2.1) arë…”

Section: Domain Wall Equations and Superpotentialmentioning

confidence: 99%

“…For 0 < r < 1 2 , the solution of (4.9) satisfying (ϕ, χ) → u 1 as x → −∞ and (ϕ, χ) → u 2 as x → ∞ has been found [3,8,9] to be given by…”

Section: A Two Scalar Field Modelmentioning

confidence: 99%

Domain wall equations, Hessian of superpotential, and Bogomol'nyi bounds

Chen

Yang

2016

Nuclear Physics B

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An important question concerning the classical solutions of the equations of motion arising in quantum field theories at the BPS critical coupling is whether all finiteenergy solutions are necessarily BPS. In this paper we present a study of this basic question in the context of the domain wall equations whose potential is induced from a superpotential so that the ground states are the critical points of the superpotential. We prove that the definiteness of the Hessian of the superpotential suffices to ensure that all finite-energy domain-wall solutions are BPS. We give several examples to show that such a BPS property may fail such that non-BPS solutions exist when the Hessian of the superpotential is indefinite. *

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“…For ε very small the minima move slightly to new positions v ε i . In this limit the tensions can be calculated as [14] τ…”

Section: Absence Of Superpotentialmentioning

confidence: 99%

Bifurcation and pattern changing with two real scalar fields

et al. 2009

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This work deals with bifurcation and pattern changing in models described by two real scalar fields. We consider generic models with quartic potentials and show that the number of independent polynomial coefficients affecting the ratios between the various domain wall tensions can be reduced to 4 if the model has a superpotential. We then study specific one-parameter families of models and compute the wall tensions associated with both BPS and non-BPS sectors. We show how bifurcation can be associated to modification of the patterns of domain wall networks and illustrate this with some examples which may be relevant to describe realistic situations of current interest in high energy physics. In particular, we discuss a simple solution to the cosmological domain wall problem.

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Exploring the vicinity of the Bogomol'nyi-Prasad-Sommerfield bound

Cited by 11 publications

References 22 publications

Defect structures in sine-Gordon like models

Defect structures in sine-Gordon like models

Domain wall equations, Hessian of superpotential, and Bogomol'nyi bounds

Bifurcation and pattern changing with two real scalar fields

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