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Letters in Mathematical Physics

, Volume 103, Issue 3, pp 299–329 | Cite as

Spectral Duality Between Heisenberg Chain and Gaudin Model

  • Andrei Mironov
  • Alexei Morozov
  • Boris Runov
  • Yegor Zenkevich
  • Andrei Zotov
Article

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 GL k Heisenberg chain is dual to the special reduced k + 2-points 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.

Mathematics Subject Classification (2010)

14H70 14H81 81Q99 

Keywords

AGT conjecture integrable systems Gaudin model integrable spin chains 

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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Andrei Mironov
    • 1
    • 2
  • Alexei Morozov
    • 2
  • Boris Runov
    • 2
    • 3
  • Yegor Zenkevich
    • 2
    • 4
  • Andrei Zotov
    • 2
  1. 1.Theory DepartmentLebedev Physics InstituteMoscowRussia
  2. 2.ITEPMoscowRussia
  3. 3.MIPT, DolgoprudniyMoscowRussia
  4. 4.Institute for Nuclear Research of the Russian Academy of SciencesMoscowRussia

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