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Séminaire de Physique Théorique
# Ding-Iohara-Miki algebra and gauge theories

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Europe/Paris

Amphithéâtre Léon Motchane (IHES)
### Amphithéâtre Léon Motchane

#### IHES

35, route de Chartres, F-91440 Bures-sur-Yvette (France)

Description

We study the role of the Ding-Iohara-Miki (DIM) algebra, which is the simplest example of quantum toroidal algebra, in gauge theories, matrix models, q-deformed CFT and refined topological strings. We use DIM algebra to write down the Ward identities for the matrix models and show how it is connected to quiver W-algebras of the A-series. We describe the integrable structure of refined topological strings arising from DIM algebra: the R-matrix, T-operators and RTT relations. Finally, we write down the q-KZ equation for the DIM algebra intertwiners and interpret its solutions as refined topological string amplitudes.

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