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arXiv · 1501.03085

Generalized spin Sutherland systems revisited

L. Feher·B. G. Pusztai
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Abstract

We present generalizations of the spin Sutherland systems obtained earlier by Blom and Langmann and by Polychronakos in two different ways: from SU(n) Yang--Mills theory on the cylinder and by constraining geodesic motion on the N-fold direct product of SU(n) with itself, for any N>1. Our systems are in correspondence with the Dynkin diagram automorphisms of arbitrary connected and simply connected compact simple Lie groups. We give a finite-dimensional as well as an infinite-dimensional derivation and shed light on the mechanism whereby they lead to the same classical integrable systems. The infinite-dimensional approach, based on twisted current algebras (alias Yang--Mills with twisted boundary conditions), was inspired by the derivation of the spinless Sutherland model due to Gorsky and Nekrasov. The finite-dimensional method relies on Hamiltonian reduction under twisted conjugations of N-fold direct product groups, linking the quantum mechanics of the reduced systems to representation theory similarly as was explored previously in the N=1 case.

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L. Feher, B. G. Pusztai. 2015-01-13. Generalized spin Sutherland systems revisited. https://doi.org/10.1016/j.nuclphysb.2015.02.003

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