

Seminar of the Department of Theoretical Physics, Steklov Mathematical Institute of RAS
December 16, 2015 14:00, Moscow, Steklov Mathematical Institute of RAS, Room 404 (8 Gubkina)






Spectral duality in gauge theories, conformal field theories and integrable systems
E. A. Zenkevich^{ab} ^{a} State Scientific Center of the Russian Federation  Institute for Theoretical and Experimental Physics, Moscow
^{b} Institute for Nuclear Research, Russian Academy of Sciences, Moscow

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Abstract:
Spectral duality has been initially put forward in the theory of integrable systems – in this setting it connects pairs of systems with the same spectral curve. One of particular cases of this duality is the Adams–Harnad–Hurtubise duality between two rational Gaudin models with different algebras and different numbers of marked points. We will consider a generalization of this duality to the case of trigonometric Gaudin models, $XXX$ and $XXZ$ spin chains. We will also show how this duality manifests itself in 4d $N=2$ supersymmetric gauge theories. In particular, we will describe its role in the AGT duality relating gauge theories with 2d CFTs. Finally, we will demonstrate how the spectral duality arises naturally in topological string theory on toric Calabi–Yau manifolds.

