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Exact multi-soliton solutions in the four dimensional Skyrme model

Exact analytic solutions of the Skyrme model defined on a spherically symmetric $R^{(1,1)} \times S^2$ geometry, chosen to mimic finite volume effects, are presented. The static and spherically symmetric configurations have non-trivial winding number and finite soliton mass. These configurations possess an extra topological charge, allowing for a novel BPS bound which can be saturated, unlike what happens in the standard case. Such solutions include exact multi-Skyrmions of arbitrary winding number, composed by interacting elementary Skyrmions. The values of the coupling constants and the compression modulus are found in good agreement with experiments by fitting the masses $M_N$ and $M_Δ$.