Skyrmions, Spectral Flow and Parity Doubles

TL;DR

This paper links the topological properties of Skyrmions to spectral flow and parity doubles, proposing new light quark dynamics and predicting novel states, supported by numerical and experimental evidence.

Contribution

It introduces a novel proof connecting Skyrmion topological charge to spectral flow, suggesting light quark effects and predicting parity doublets in nuclear spectra.

Findings

Identification of baryon number via spectral flow

Prediction of a (1/2)^{-} state and its excitations

Evidence for parity doublets in light nuclei

Abstract

It is well-known that the winding number of the Skyrmion can be identified as the baryon number. We show in this paper that this result can also be established using the Atiyah-Singer index theorem and spectral flow arguments. We argue that this proof suggests that there are light quarks moving in the field of the Skyrmion. We then show that if these light degrees of freedom are averaged out, the low energy excitations of the Skyrmion are in fact spinorial. A natural consequence of our approach is the prediction of a $(1/2)^{-}$ state and its excitations in addition to the nucleon and delta. Using the recent numerical evidence for the existence of Skyrmions with discrete spatial symmetries, we further suggest that the the low energy spectrum of many light nuclei may possess a parity doublet structure arising from a subtle topological interaction between the slow Skyrmion and the fast quarks. We also present tentative experimental evidence supporting our arguments.