Spectral duality in integrable systems from AGT conjecture
A. Mironov+*, A. Morozov*, Y. Zenkevich*×°, A. Zotov*
+Theory Department, Lebedev Physics Institute, 119991 Moscow, Russia
*Alikhanov Institute for Theoretical and Experimental Physics, 117218 Moscow, Russia
×Physical Department, Lomonosov Moscow State University, 119234 Moscow, Russia
°Institute for Nuclear Research of the RAS, 117312 Moscow, Russia
We describe relationships between integrable systems with N degrees of freedom arising from the AGT conjecture. Namely, we
prove the equivalence (spectral duality) between the N-cite Heisenberg spin chain and a reduced glN Gaudin model
both at classical and quantum level. The former one appears on the gauge theory side of the AGT relation in the
Nekrasov-Shatashvili (and further the Seiberg-Witten) limit while the latter one is natural on the CFT side. At the classical
level, the duality transformation relates the Seiberg-Witten differentials and spectral curves via a bispectral involution.
The quantum duality extends this to the equivalence of the corresponding Baxter-Schrödinger equations (quantum spectral
curves). This equivalence generalizes both the spectral self-duality between the 2× 2 and N× N representations
of the Toda chain and the famous AHH duality.