Fractional Skyrmion molecules in a \u2102PN\u22121 model

Yutaka Akagi,Muneto Nitta,Yuki Amari,Yakov Shnir,Sven Bjarke Gudnason

doi:10.1007/jhep11(2021)194

Abstract

We study fractional Skyrmions in a ℂP2 baby Skyrme model with a generalization of the easy-plane potential. By numerical methods, we find stable, metastable, and unstable solutions taking the shapes of molecules. Various solutions possess discrete symmetries, and the origin of those symmetries are traced back to congruencies of the fields in homogeneous coordinates on ℂP2.

Highlights

A single SU(N ) Yang-Mills instanton on R3 × S1 with a twisted boundary condition along S1 is decomposed into N fractional instantons with induced monopole charges that sum to zero [89], while a single CP N−1 NLσ model instanton (Skyrmion instanton in the SU(N ) principal chiral model) on R1 × S1 (R2 × S1) with a twisted boundary condition along S1 is decomposed into N fractional instantons with induced domain wall charges that sum to zero [90,91,92,93,94,95] ([96])
We have studied fractional Skyrmions in a CP 2 baby Skyrme model made of the standard kinetic term, the Skyrme term generalized to CP 2 and a generalization of the easy-plane potential
The solutions we have found are all molecules of N Q fractional Skyrmions with each constituent carrying 1/N of the topological charge Q

Summary

The model

We investigate static solutions of the CP 2 baby Skyrme type model (1.1) with the potential (1.3). N 2 − 1, na must vanish at spatial infinity) This condition effectively compactifies physical space, R2, to the 2-sphere, i.e. R2 ∪ {∞} S2, and a static configuration with finite energy corresponds to a map from S2 to CP N−1. Such configurations are characterized by the topological charge. The fields na enable us to interpret the physical meaning of the components in the Lagrangian or energy functional They do not appear to be the best option for constructing solutions because of their complicated nonlinear constraints given in eq (1.2). On the other hand, when the mapping is two-dimensional, the configuration is a full map to CP 2

Numerical solutions

Summary and discussion