Multi-Skyrmions on $AdS_2 \times S_2$, Rational maps and Popcorn Transitions

TL;DR

This paper constructs multi-Skyrmion solutions in $AdS_2 imes S_2$ using combined techniques, revealing how increased charge density favors multi-layered configurations, akin to holographic popcorn transitions.

Contribution

It introduces a novel method combining generalized hedgehog and rational map ansatz to find multi-Skyrmion configurations in $AdS_2 imes S_2$ and explores their energetic preferences.

Findings

Multi-layered Skyrmion configurations are energetically favored at high charge density.

The total Baryon charge is a product of radial kinks and rational map degree.

High charge density leads to configurations with more peaks and lower rational map degree.

Abstract

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.