Near-BPS baby Skyrmions with Gaussian tails

Abstract We consider the baby Skyrme model in a physically motivated limit of reaching the restricted or BPS baby Skyrme model, which is a model that enjoys area-preserving diffeomorphism invariance. The perturbation consists of the kinetic Dirichlet term with a small coefficient ϵ as well as the standard pion mass term, with coefficient $$ \upepsilon {m}_1^2 $$ ϵ m 1 2 . The pions remain lighter than the soliton for any ϵ and therefore the model is physically acceptable, even in the ϵ → 0 limit. The version of the BPS baby Skyrme model we use has BPS solutions with Gaussian tails. We perform full numerical computations in the ϵ → 0 limit and even reach the strict ϵ = 0 case, finding new nontrivial BPS solutions, for which we do not yet know the analytic form.

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Near-BPS baby Skyrmions

Journal of High Energy Physics ◽

10.1007/jhep11(2020)062 ◽

2020 ◽

Vol 2020 (11) ◽

Cited By ~ 2

Author(s):

Sven Bjarke Gudnason ◽

Marco Barsanti ◽

Stefano Bolognesi

Keyword(s):

Binding Energy ◽

Topological Charge ◽

Harmonic Maps ◽

Single Point ◽

Pion Mass ◽

Mass Term ◽

Skyrme Model ◽

Classical Solutions ◽

Leading Order ◽

Area Preserving

Abstract We consider the baby-Skyrme model in the regime close to the so-called restricted baby-Skyrme model, which is a BPS model with area-preserving diffeomorphism invariance. The perturbation takes the form of the standard kinetic Dirichlet term with a small coefficient ϵ. Classical solutions of this model, to leading order in ϵ, are called restricted harmonic maps. In the BPS limit (ϵ → 0) of the model with the potential being the standard pion-mass term, the solution with unit topological charge is a compacton. Using analytical and numerical arguments we obtain solutions to the problem for topological sectors greater than one. We develop a perturbative scheme in ϵ with which we can calculate the corrections to the BPS mass. The leading order ($$ \mathcal{O}\left({\upepsilon}^1\right) $$ O ϵ 1 ) corrections show that the baby Skyrmion with topological charge two is energetically preferred. The binding energy requires us to go to the third order in ϵ to capture the relevant terms in perturbation theory, however, the binding energy contributes to the total energy at order ϵ2. We find that the baby Skyrmions — in the near-BPS regime — are compactons of topological charge two, that touch each other on their periphery at a single point and with orientations in the attractive channel.

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Finkelstein–Rubinstein constraints for the Skyrme model with pion masses

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2006.1664 ◽

2006 ◽

Vol 462 (2071) ◽

pp. 2001-2016 ◽

Cited By ~ 11

Author(s):

Steffen Krusch

Keyword(s):

Nuclear Physics ◽

Pion Mass ◽

Classical Field Theory ◽

Mass Term ◽

Baryon Number ◽

Skyrme Model ◽

Classical Field ◽

Rational Maps ◽

Rational Map ◽

Atomic Nuclei

The Skyrme model is a classical field theory modelling the strong interaction between atomic nuclei. It has to be quantized in order to compare it to nuclear physics. When the Skyrme model is semi-classically quantized it is important to take the Finkelstein–Rubinstein constraints into account. Recently, a simple formula has been derived to calculate the constraints for Skyrmions which are well approximated by rational maps. However, if a pion mass term is included in the model, Skyrmions of sufficiently large baryon number are no longer well approximated by the rational map ansatz. This paper addresses the question how to calculate Finkelstein–Rubinstein constraints for Skyrme configurations which are only known numerically.

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A stealth defect of spacetime

Modern Physics Letters A ◽

10.1142/s0217732318501274 ◽

2018 ◽

Vol 33 (22) ◽

pp. 1850127 ◽

Cited By ~ 2

Author(s):

F. R. Klinkhamer ◽

J. M. Queiruga

Keyword(s):

Energy Density ◽

Long Range ◽

Mass Term ◽

Matter Field ◽

Skyrme Model ◽

Gravitational Mass ◽

Positive Energy ◽

Type Solution ◽

Matter Fields

We discuss a special type of Skyrmion spacetime-defect solution, which has a positive energy density of the matter fields but a vanishing asymptotic gravitational mass. With a mass term for the matter field added to the action (corresponding to massive “pions” in the Skyrme model), this particular soliton-type solution has no long-range fields and can appropriately be called a “stealth defect”.

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Effective pion mass term and the trace anomaly

Physical Review D ◽

10.1103/physrevd.95.016003 ◽

2017 ◽

Vol 95 (1) ◽

Cited By ~ 7

Author(s):

Maarten Golterman ◽

Yigal Shamir

Keyword(s):

Pion Mass ◽

Mass Term ◽

Trace Anomaly

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The 1-soliton in theSO(3) gauged Skyrme model with mass term

Nonlinearity ◽

10.1088/0951-7715/15/2/308 ◽

2002 ◽

Vol 15 (2) ◽

pp. 385-392 ◽

Cited By ~ 4

Author(s):

Y Brihaye ◽

J Burzlaff ◽

V Paturyan ◽

D H Tchrakian

Keyword(s):

Mass Term ◽

Skyrme Model

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Steady Euler flows and the Faddeev-Skyrme model with mass term

Journal of Mathematical Physics ◽

10.1063/1.4907922 ◽

2015 ◽

Vol 56 (2) ◽

pp. 023102 ◽

Cited By ~ 3

Author(s):

Radu Slobodeanu

Keyword(s):

Mass Term ◽

Skyrme Model ◽

Euler Flows

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Hamiltonian formulation of higher rank symmetric gauge theories

The European Physical Journal C ◽

10.1140/epjc/s10052-021-09964-2 ◽

2022 ◽

Vol 82 (1) ◽

Author(s):

Rabin Banerjee

Keyword(s):

Gauge Theories ◽

Hamiltonian Formulation ◽

Diffeomorphism Invariance ◽

Lowest Landau Level ◽

Level Problem ◽

Higher Rank ◽

New Form ◽

Area Preserving ◽

Symmetric Gauge

AbstractRecent discussions of fractons have evolved around higher rank symmetric gauge theories with emphasis on the role of Gauss constraints. This has prompted the present study where a detailed hamiltonian analysis of such theories is presented. Besides a general treatment, the traceless scalar charge theory is considered in details. A new form for the action is given which, in $$2+1$$ 2 + 1 dimensions, yields area preserving diffeomorphisms. Investigation of global symmetries reveals that this diffeomorphism invariance induces a noncommuting charge algebra that gets exactly mapped to the algebra of coordinates in the lowest Landau level problem. Connections of this charge algebra to noncommutative fluid dynamics and magnetohydrodynamics are shown.

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