Spin Statistics and Surgeries of Topological Solitons in QCD Matter in Magnetic Field

TL;DR

This paper investigates the spin statistics of topological solitons in QCD matter under strong magnetic fields, revealing their fermionic or bosonic nature based on quantization and proposing surgical transformations among them.

Contribution

It introduces two methods to determine the spin statistics of topological solitons in QCD, and proposes novel surgeries transforming solitons into different topological states.

Findings

Pancake solitons and holes are fermions or bosons depending on surface area quantization.

Domain-wall Skyrmions are identified as bosons.

Surgical transformations connect different topological solitons.

Abstract

The ground state of QCD with two flavors (up and down quarks) at finite baryon density in sufficiently strong magnetic field is in a form of either a chiral soliton lattice(CSL), an array of solitons stacked along the magnetic field, or a domain-wall Skyrmion phase in which Skyrmions are spontaneously created on top of the CSL In the latter, one 2D (baby) Skyrmion in the chiral soliton corresponds to two 3D Skyrmions (baryons) in the bulk. In this paper, we study spin statistics of topological solitons by using the following two methods: the conventional Witten's method by embedding the pion fields of two flavors into those of three flavors with the Wess-Zumino-Witten (WZW) term, and a more direct method by using the two-flavor WZW term written in terms of a spin structure. We find that a chiral soliton of finite quantized size called a pancake soliton and a hole on a chiral soliton are fermions or bosons depending on odd or even quantizations of their surface areas, respectively, and a domain-wall Skyrmion is a boson. We also propose surgeries of topological solitons: a domain-wall Skyrmion (boson) can be cut into a pancake soliton (fermion) and a hole (fermion), and a chiral soliton without Skyrmions can be cut into a pancake soliton (fermion) and a hole (fermion).