Self-duality of the compactified Ruijsenaars-Schneider system from quasi-Hamiltonian reduction

L. Fehér, C. Klimčík

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

The Delzant theorem of symplectic topology is used to derive the completely integrable compactified Ruijsenaars-Schneider III b system from a quasi-Hamiltonian reduction of the internally fused double SU(n)×SU(n). In particular, the reduced spectral functions depending respectively on the first and second SU(n) factor of the double engender two toric moment maps on the III b phase space CP(n-1) that play the roles of action-variables and particle-positions. A suitable central extension of the SL(2,Z) mapping class group of the torus with one boundary component is shown to act on the quasi-Hamiltonian double by automorphisms and, upon reduction, the standard generator S of the mapping class group is proved to descend to the Ruijsenaars self-duality symplectomorphism that exchanges the toric moment maps. We give also two new presentations of this duality map: one as the composition of two Delzant symplectomorphisms and the other as the composition of three Dehn twist symplectomorphisms realized by Goldman twist flows. Through the well-known relation between quasi-Hamiltonian manifolds and moduli spaces, our results rigorously establish the validity of the interpretation [going back to Gorsky and Nekrasov] of the III b system in terms of flat SU(n) connections on the one-holed torus.

Original languageEnglish
Pages (from-to)464-515
Number of pages52
JournalNuclear Physics B
Volume860
Issue number3
DOIs
Publication statusPublished - Jul 21 2012

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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