JHEP, 2013, Issue 12, 034, 11 pp.
Spectral dualities in XXZ spin chains and five dimensional gauge theories
A. Mironovab, A. Morozova, B. Runovac, Y. Zenkevichad, A. Zotoveac
a Institute for Theoretical and Experimental Physics (ITEP),
b Theory Department, Lebedev Physics Institute,
c Moscow Institute of Physics and Technology (MIPT),
Dolgoprudniy, Moscow, Russia
d Institute for Nuclear Research of the Russian Academy of Sciences,
e Steklov Mathematical Institute of the Russian Academy of Sciences,
Motivated by recent progress in the study of supersymmetric gauge theories we propose a very compact formulation of spectral duality between XXZ spin chains. The action of the quantum duality is given by the Fourier transform in the spectral parameter. We investigate the duality in various limits and, in particular, prove it for $q\to1$, i.e. when it reduces to the XXX/Gaudin duality. We also show that the universal difference operators are given by the normal ordering of the classical spectral curves.
|Ministry of Education and Science of the Russian Federation
|Russian Foundation for Basic Research
|Our work was partly supported by Ministry of Education and Science of the Russian Federation under contract 8498, the Brazil National Counsel of Scientific and Technological Development (A.Mor.), by NSh-3349.2012.2 (A.Mir., A.Mor.), by RFBR grants 14-02-92009, 13-02-00457 (A.Mir.), 13-02-00478 (A.Mor., Y.Z.), 12-02-31595 (Y.Z.) and 12-01-00482 (B.R., A.Z.), by joint grants 12-02-92108-Yaf (A.Mir., A.Mor.), 13-02-91371-ST (A.Mir., A.Mor., B.R.), 14-01-93004-Viet (A.Mir., A.Mor.), by leading young scientific groups RFBR 12-01-33071 mol a ved (B.R., Y.Z., A.Z.) and by D. Zimin’s “Dynasty”
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