Multi-Skyrmions on AdS2 × S2, rational maps and popcorn transitions

By combining two different techniques to construct multi-soliton solutions of the (3+1)-dimensional Skyrme model, the generalized hedgehog and the rational map ansatz, we find multi-Skyrmion configurations in AdS2×S2. We construct Skyrmionic multi-layered configurations such that the total Baryon charge is the product of the number of kinks along the radial AdS2 direction and the degree of the rational map. We show that, for fixed total Baryon charge, as one increases the charge density on ∂(AdS2×S2), it becomes increasingly convenient energetically to have configurations with more peaks in the radial AdS2 direction but a lower degree of the rational map. This has a direct relation with the so-called holographic popcorn transitions in which, when the charge density is high, multi-layered configurations with low charge on each layer are favored over configurations with few layers but with higher charge on each layer. The case in which the geometry is M2×S2 can also be analyzed.