Spectral duality in integrable systems from AGT conjecture
Abstract
We describe relationships between integrable systems with N degrees of freedom arising from the Alday-Gaiotto-Tachikawa 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 Alday-Gaiotto-Tachikawa 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 Adams-Harnad-Hurtubise duality.
- Publication:
-
Soviet Journal of Experimental and Theoretical Physics Letters
- Pub Date:
- March 2013
- DOI:
- 10.1134/S0021364013010062
- arXiv:
- arXiv:1204.0913
- Bibcode:
- 2013JETPL..97...45M
- Keywords:
-
- JETP Letter;
- High Energy Phys;
- Conformal Block;
- Spectral Curve;
- Spectral Curf;
- High Energy Physics - Theory;
- Mathematical Physics;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- Pis'ma v ZhETF 97 (2013) 49-56