Skyrmions, spectral flow and parity doubles

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 es tablished using the Atiyah-Singer index theorem and spectral flow arguments . We argue that this proof suggests that there are light quarks moving in t he field of the Skyrmion. We then show that if these light degrees of freed om 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 sub tle topological interaction between the slow Skyrmion and the fast quarks. We also present tentative experimental evidence supporting our arguments.