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.