Fermions, Skyrmions and the 3-Sphere

TL;DR

This paper analyzes fermions coupled to Skyrmions on a 3-sphere, deriving explicit solutions, energy spectra, and degeneracies, and discusses the Dirac sea energy using zeta function regularization.

Contribution

It provides explicit solutions and energy spectra for fermions coupled to Skyrmions on a 3-sphere, including non-zero grand spin cases, and explores the Dirac sea energy.

Findings

Explicit solutions for fermions with Skyrme background on 3-sphere.

Derived energy spectra and degeneracies for all grand spin values.

Analyzed Dirac sea energy using zeta function regularization.

Abstract

This paper investigates a background charge one Skyrme field chirally coupled to light fermions on the 3-sphere. The Dirac equation for the system commutes with a generalised angular momentum or grand spin. It can be solved explicitly for a Skyrme configuration given by the hedgehog form. The energy spectrum and degeneracies are derived for all values of the grand spin. Solutions for non-zero grand spin are each characterised by a set of four polynomials. The paper also discusses the energy of the Dirac sea using zeta function regularization.