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This article is cited in 59 scientific papers (total in 59 papers)
Spectral duality between Heisenberg chain and Gaudin model
A. Mironovab, A. Morozova, B. Runovac, E. Zenkevichad, A. Zotova a ITEP, Moscow, Russia
b Theory Department, Lebedev Physics Institute, Moscow, Russia
c MIPT, Dolgoprudniy, Moscow, Russia
d Institute for Nuclear Research of the Russian Academy of Sciences, Moscow, Russia
Abstract:
In our recent paper we described relationships between integrable systems
inspired by the AGT conjecture. On the gauge theory side an integrable spin chain naturally
emerges while on the conformal field theory side one obtains some special reduced
Gaudin model. Two types of integrable systems were shown to be related by the spectral
duality. In this paper we extend the spectral duality to the case of higher spin chains. It
is proved that the $N$-site $\mathrm{GL}_k$ Heisenberg chain is dual to the special reduced $k+2$-points
$\mathrm{gl}_N$ Gaudin model. Moreover, we construct an explicit Poisson map between the models
at the classical level by performing the Dirac reduction procedure and applying the AHH
duality transformation.
Received: 03.07.2012 Revised: 05.11.2012 Accepted: 06.11.2012
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