TL;DR
This paper explores the interaction between fermions and Skyrmions on a 3-sphere, providing explicit solutions for certain configurations and analyzing spectral changes caused by topological features.
Contribution
It offers explicit solutions for fermions coupled to Skyrmions on S^3 and investigates spectral effects of non-trivial winding numbers both analytically and numerically.
Findings
Explicit solutions for G=0 cases with constant and hedgehog Skyrme configurations
Spectral changes due to non-trivial winding numbers
Numerical analysis of general Skyrme configurations
Abstract
This paper discusses Skyrmions on the 3-sphere coupled to fermions. The resulting Dirac equation commutes with a generalized angular momentum G. For G = 0 the Dirac equation can be solved explicitly for a constant Skyrme configuration and also for a SO(4) symmetric hedgehog configuration. We discuss how the spectrum changes due to the presence of a non-trivial winding number, and also consider more general Skyrme configurations numerically.
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