Cours de l'IHÉS 2014-2015
# Supersymmetric Vacua and Integrability (1/3)

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

#### IHES

Le Bois-Marie
35, route de Chartres
91440 Bures-sur-Yvette

Description

I review the relationship between supersymmetric gauge theories and quantum integrable systems. From the quantum integrability side this relation includes various spin chains, as well as many well-known quantum many body systems like elliptic Calogero-Moser system and generalisations. From the gauge theory side one has supersymmetric gauge theories with four (and eight) supercharges in various space-time dimensions (compactified to two-dimensions, or in Omega-background). Gauge theory perspective provides the exact energy spectrum of corresponding quantum integrable system. Key elements, usually appearing in the topic of quantum integrability, such as Baxter equation, Yang-Yang function, Bethe equation, spectral curve, Yangian, quantum affine algebra, quantum elliptic algebra - all acquire meaning in the supersymmetric gauge theory.

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