Quantum Seiberg-Witten curve and q-deformed W(infinity) algebra

Yutaka Matsuo

Tokyo University

Mon, Oct. 10th 2016, 11:00

Salle Claude Itzykson, Bât. 774, Orme des Merisiers

A few years ago, Nekrasov and his collaborators proposed a double quantum deformation of Seiberg-Witten curve with omega background parameters which describes 4D and 5D supersymetric gauge theories. It illuminates not only the quantization of geometry but also gives an intimate relation with integrable models. \ par In this talk, we present a purely algebraic derivation of his proposal, based on the quantum deformation of W(infinity) algebra. We introduced the building blocks of Nekrasov partition function, Gaiotto state, intertwiner and so on, and a simple characterization of such states and operators. It gives the qq-deformed SW curve in the form of Ward identities. The connection with the integrable models associated with 2D CFT will be also explained in some detail.

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