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 A d S 2 × S 2 . We construct Skyrmionic multi-layered configurations such that the total Baryon charge is the product of the number of kinks along the radial A d S 2 direction and the degree of the rational map. We show that, for fixed total Baryon charge, as one increases the charge density on ? ( A d S 2 × S 2 ) , it becomes increasingly convenient energetically to have configurations with more peaks in the radial A d S 2 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 M 2 × S 2 can also be analyzed.
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机译：通过组合两种不同的技术来构造（3 +1）维Skyrme模型的多孤子解，广义刺猬和有理图ansatz，我们发现A d S 2×S 2中的多Skyrmion构型。我们构造了Skyrmionic多层结构，以使总重子电荷是沿径向A d S 2方向的扭结数与有理图的度数的乘积。我们证明，对于固定的重子总电荷，随着increases的增加，电荷密度增加。 （A d S 2×S 2），具有在径向A d S 2方向上具有更多峰但具有较低有理图度的构造在能量上变得越来越方便。这与所谓的全息爆米花转变有直接关系，在全息爆米花转变中，当电荷密度高时，每层上电荷低的多层构型比很少层但每层电荷高的构型更为有利。还可以分析几何形状为M 2×S 2的情况。
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