Spectral Duality Between Heisenberg Chain and Gaudin Model

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.

36 pages

References in corpus (4)

• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• Nekrasov prepotential with fundamental matter from the quantum spin chain
• Monopoles and Modifications of Bundles over Elliptic Curves
• A quantum isomonodromy equation and its application to N=2 SU(N) gauge theories

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