

Seminar of the Department of Theoretical Physics, Steklov Mathematical Institute of RAS
November 18, 2015 14:00, Moscow, Steklov Mathematical Institute of RAS, Room 404 (8 Gubkina)






Quantum spectral curve for $(q,t)$matrix model and XXZ spin chain
E. A. Zenkevich^{ab} ^{a} Institute for Nuclear Research, Russian Academy of Sciences, Moscow
^{b} State Scientific Center of the Russian Federation  Institute for Theoretical and Experimental Physics, Moscow

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Abstract:
In the large $N$ limit the properties of matrix models are generally governed by their spectral curves. For some models there is a natural deformation of this setup to the more general Nekrasov–Shatashvili limit. This deformation corresponds to quantization of the spectral curve, which can be interpreted as an operator acting on the wave function of a finite dimensional integrable system in separated variables. We consider the realisation of these ideas in the case of the $(q,t)$matrix model (also known as the $q$deformed betaensemble), where the quantum spectral curve turns out to be certain difference operator and the corresponding integrable system is the closed inhomogeneous XXZ spin chain. We also discuss the relation between our results, AGT duality and spectral duality in integrable systems, CFT and gauge theories.

