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We describe relationships between integrable systems with N degrees offreedom arising from the AGT conjecture. Namely, we prove the equivalence(spectral duality) between the N-cite Heisenberg spin chain and a reduced gl(N)Gaudin model both at classical and quantum level. The former one appears on thegauge theory side of the AGT relation in the Nekrasov-Shatashvili (and furtherthe Seiberg-Witten) limit while the latter one is natural on the CFT side. Atthe classical level, the duality transformation relates the Seiberg-Wittendifferentials and spectral curves via a bispectral involution. The quantumduality extends this to the equivalence of the corresponding Baxter-Schrodingerequations (quantum spectral curves). This equivalence generalizes both thespectral self-duality between the 2x2 and NxN representations of the Toda chainand the famous AHH duality.

Spectral Duality in Integrable Systems from AGT Conjecture