BPS skyrmions of generalized Skyrme model in higher dimensions

Abstract

In this work we consider the higher dimensional Skyrme model, with spatial dimension d > 3, focusing on its BPS submodels and their corresponding features. To accommodate the cases with a higher topological degree, B ≥ 1, a modified generalized hedgehog ansatz is used where we assign an integer ni for each rotational plane, resulting in a topological degree that proportional to product of these integers. It is found via BPS Lagrangian method that there are only two possible BPS submodels for this spherically symmetric ansatz which shall be called as BPS Skyrme model and scale-invariant model. The properties of the higher dimensional version of both submodels are studied and it is found that the BPS Skyrmions with B ≥ 1 exist in the first submodel but there is only B = 1 BPS Skyrmion in the second submodel. We also study the higher dimensional version of self-duality conditions in terms of strain tensor eigenvalues and find that, in general, the scale-invariant model has a stronger self-duality condition than the BPS Skyrme model.

Bogomol’nyi-like equations in gravity theories

“…As an example in three dimensional Maxwell-Chern-Simons-Higgs model, using non-boundary BPS Lagrangian gave us the usual BPS vortices, without internal pressures, but with a less degree of freedom, by means one of the effective fields depend on the other effective field [23]. Another examples of using non-boundary BPS Lagrangian density have been discussed in the generalized Skyrme model and its higher dimensional extensions [24][25][26]. All those examples depend on some particular ansatzes which are mainly choosen by a requirement that the Bogomol'nyi equations must be spherically symmetric.…”

“…In these cases we need to identify the effective Lagrangian density and its effective fields such that its Euler-Lagrange equations, for the effective fields, are effectively equal to the original Euler-Lagrange equations for the fundamental fields written under the corresponding ansatz. For the cases considered here the effective Lagrangian density for gravity parts are simply obtained by imposing the ansatz (27), after identifying the effective fields, into the action (26). Knowing the correct effective fields is important for deriving the constraint equations from the BPS Lagrangian density.…”