Seminar “Modern Mathematical Physics”

Date and Time: Thursday, 23 August 2018, at 3:30 PM

Venue: Blokhintsev Hall (4th floor), Bogoliubov Laboratory of Theoretical Physics

Seminar topic: «Quantum aspects of Skyrme-type models: How Skyrmions acquire the spin?»

Speaker: Nobuyuki Sawado (Tokyo University of Sciences)

Abstract:

I discuss quantum aspects of some Skyrme-type solitons. The Skyrme model is a model hadrons after a suitable quantization such as the collective coordinate approximation is implemented. The Wess-Zumino action obeys a quantization law of which the prefactor is the number of quark colors (i.e. of the degeneracy). The model with the explicit quark degrees of freedom is usable to study interior structure of the hadrons such as parton distribution. Also, the spin-statistical nature is well understood by studying the normalizable modes of quarks supported by the index theorem. The two-dimensional version, the baby-Skyrme model or CPN Skyrme-Faddeev model, possess planar soliton solutions.

For N=1 it is believed that the quantum aspects exhibit a special property, so called the fractional spin θ/2π , (0 ≤ θ ≤ π), when the Hopf term is added in the action of the model. For the point of view of a fermionic model coupled with the baby-skyrmions, however, no ambiguity by θ appears. An analogue of the Wess-Zumino term appears in CPN field which plays a similar role as the Hopf term, and now the soliton has to be quantized as an anyon even if normalizable fermions are taken into account. I would like to discuss the issues through the heat kernel expansion and also the spectral flow argument.

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