Topological energy bounds for the Skyrme and Faddeev models with massive pions

Harland, Derek

doi:10.1016/j.physletb.2013.11.062

Cited by 58 publications

(75 citation statements)

References 23 publications

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“…The geometrical reason why the R 3 and S 3 cases are so distinct is the following. The bound can be saturated if and only if the three eigenvalues of the corresponding strain tensor are 1) all equal and 2) constant which means that the corresponding map must be an isometry [23]. This is a very restrictive condition which, for the target space S 3 , may be fulfilled only if the base space is also a three-sphere.…”

Section: E 4 Modelmentioning

confidence: 99%

Skyrme models and nuclear matter equation of state

2015

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We investigate the role of pressure in a class of generalised Skyrme models. We introduce pressure as the trace of the spatial part of the energy-momentum tensor and show that it obeys the usual thermodynamical relation. Then, we compute analytically the mean-field equation of state in the high and medium pressure regimes by applying topological bounds on compact domains. The equation of state is further investigated numerically for the charge one skyrmions. We identify which term in a generalised Skyrme model is responsible for which part in the equation of state. Further, we compare our findings with the corresponding results in the Walecka model.

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Section: E 4 Modelmentioning

confidence: 99%

Skyrme models and nuclear matter equation of state

2015

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“…Binding energies can then be made suitably small by choosing the value of the interpolation parameter sufficiently close to the repulsive limit. An appropriate repulsive theory in three dimensions has recently been identified and consists of a Skyrme term and a potential term, chosen so that a topological energy bound can be attained only in the onesoliton sector [6]. This makes the above interpolation scheme feasible and work is currently underway to investigate this in detail [7].…”

Section: Introductionmentioning

confidence: 99%

Aloof baby Skyrmions

Salmi¹,

Sutcliffe²

2014

J. Phys. A: Math. Theor.

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We show that a suitable choice for the potential term in the two-dimensional baby Skyrme model yields solitons that have a short-range repulsion and a long-range attraction. The solitons are therefore aloof, in the sense that static multi-soliton bound states have constituents that preserve their individual identities and are sufficiently far apart that tail interactions yield small binding energies. The static multi-soliton solutions are found to have a cluster structure that is reproduced by a simple binary species particle model. In the standard three-dimensional Skyrme model of nuclei, solitons are too tightly bound and are often too symmetric, due to symmetry enhancement as solitons coalesce to form bound states. The aloof baby Skyrmion results endorse a way to resolve these issues and provides motivation for a detailed study of the related three-dimensional version of the Skyrme model.

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“…Moving to an extreme parameter regime in the standard Skyrme model, where the quartic Skyrme term dominates over the usual leading order quadratic term, allows a potential term to significantly influence the properties of Skyrmions [20]. This has been exploited by making a non-standard choice of the potential term to produce a lightly bound Skyrme…”

Section: Jhep05(2018)174mentioning

confidence: 99%

Skyrmions in models with pions and rho mesons

Naya

Sutcliffe

2018

J. High Energ. Phys.

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A problem with the standard Skyrme model is that Skyrmion binding energies are around 15%, being much larger than the order 1% binding energies of the nuclei that they aim to describe. Here we consider theories that extend the standard Skyrme model of pions by including rho mesons, via dimensional deconstruction of Yang-Mills theory with an extra dimension. We report the first results of parallel numerical computations of multiSkyrmions in theories of this type, including a model that reduces Skyrmion energies below those of the standard Skyrme model whilst retaining exactly the same Faddeev-Bogomolny energy bound. We compute all Skyrmions with baryons numbers up to 12 and find that the inclusion of rho mesons reduces binding energies to less than 4%, and therefore moves Skyrmion theory closer to experimental data. Furthermore, we find that this dramatic reduction in binding energies is obtained without changing the qualitative features of the Skyrmions, such as their symmetries.

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Topological energy bounds for the Skyrme and Faddeev models with massive pions

Cited by 58 publications

References 23 publications

Skyrme models and nuclear matter equation of state

Skyrme models and nuclear matter equation of state

Aloof baby Skyrmions

Skyrmions in models with pions and rho mesons

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