A generalized false vacuum Skyrme model

Abstract We propose a generalization of the False Vacuum Skyrme model for any simple compact Lie group G . Now the Skyrme field is a map U : R 3 , 1 → G , while the remaining fields correspond to the entries of a symmetric, positive, and invertible dim ⁡ G × dim ⁡ G -dimensional matrix h . We prove that the global minima correspond to the h fields being self-dual solutions of the generalized BPS Skyrme model, together with a particular field configuration for the Skyrme field that leads to a spherically symmetric topological charge density. As in the case of the original model, the minimization of the energy leads to the so-called Coleman’s reduced problem, defined in the context of false vacuum decay. This imposes a condition on the Skyrme field, which, if satisfied, makes the total energy of the global minima, as well as the main properties of the model, equivalent to those obtained for the G = S U ( 2 ) case. We study this condition and its consequences within the generalized rational map ansatz and show how it can be satisfied for G = S U ( p + q ) , where p and q are positive integers, with the Hermitian symmetric spaces being S U ( p + q ) / ( S U ( p ) ⊗ S U ( q ) ⊗ U ( 1 ) ) . We also provide a numerical study of the baryon density, root-mean-square radius, and binding energy that deepens previously analysis for the S U ( 2 ) False Vacuum Skyrme model. Additionally, in the case of G = S