$AdS_2 \times S_2$上的多Skyrmions、有理映射和Popcorn变换
Multi-Skyrmions on $AdS_2 \times S_2$, Rational maps and Popcorn Transitions
摘要：
通过结合两种不同的构造（3+1）维Skyrme模型多孤子解的方法，即广义hedgehog和有理映射方法，我们在$AdS_{2}\times S_{2}$中发现了多Skyrmion组态.我们构造了Skyrmionic多层组态，使得重子总电荷是沿径向$AdS_{2}$方向的扭结数与有理映射度的乘积.我们发现，对于固定的总重子电荷，随着$\partial\left( AdS_{2}\times S_{2}\right) $上电荷密度的增加，在能量上变得越来越方便，在径向$AdS_{2}$方向上具有更多峰的构型，但理性映射的程度较低。这与所谓的全息爆米花转变有直接关系，其中当电荷密度高时，每层上具有低电荷的多层配置优于具有较少层但每层上具有较高电荷的配置。也可以分析几何形状为$M_{2}\times S_{2}$的情况。
英文摘要：
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 $AdS_{2}\times S_{2}$. We construct Skyrmionic multi-layered configurations such that the total Baryon charge is the product of the number of kinks along the radial $AdS_{2}$ direction and the degree of the rational map. We show that, for fixed total Baryon charge, as one increases the charge density on $\partial\left( AdS_{2}\times S_{2}\right) $, it becomes increasingly convenient energetically to have configurations with more peaks in the radial $AdS_{2}$ 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 $M_{2}\times S_{2}$ can also be analyzed.
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