Skyrmions, Spectral Flow and Parity Doubles

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.

22 pages, LaTex. Uses amstex, amssymb

References in corpus (3)

• Rational Maps, Monopoles and Skyrmions
• Symmetric Skyrmions
• On the Parity Degeneracy of Baryons

Cited by in corpus (9)

• Parity doubling in particle physics
• Zero mode quantization of multi-Skyrmions
• Mixed States from Anomalies
• Soliton solutions of the fermion-Skyrmion system in (2+1) dimensions
• Quantum Gravity: Mixed States from Diffeomorphism Anomalies
• Fermions coupled to Skyrmions on S^3
• Degeneracy of the quarks, shell structure in the chiral soliton
• Axially symmetric multi-baryon solutions and their quantization in the chiral quark soliton model
• Fermions, Skyrmions and the 3-Sphere