On the Integrability of Four Dimensional N=2 Gauge Theories in the Omega Background

Abstract

We continue to investigate the relationship between the infrared physics of N=2 supersymmetric gauge theories in four dimensions and various integrable models such as Gaudin, Calogero-Moser and quantum spin chains. We prove interesting dualities among some of these integrable systems by performing different, albeit equivalent, quantizations of the Seiberg-Witten curve of the four dimensional theory. We also discuss conformal field theories related to N=2 4d gauge theories by the Alday-Gaiotto-Tachikawa (AGT) duality and the role of conformal blocks of those CFTs in the integrable systems. As a consequence, the equivalence of conformal blocks of rank two Toda and Novikov-Wess-Zumino-Witten (WZNW) theories on the torus with punctures is found.

37 pages, 10 figures, references added, figures modified, JHEP version

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Cited by in corpus (9)

• Spectral dualities in XXZ spin chains and five dimensional gauge theories
• A slow review of the AGT correspondence
• Intersecting defects in gauge theory, quantum spin chains, and Knizhnik-Zamolodchikov equations
• Mayer-Cluster Expansion of Instanton Partition Functions and Thermodynamic Bethe Ansatz
• Fiber-base duality from the algebraic perspective
• On Quiver W-algebras and Defects from Gauge Origami
• A pedagogical introduction to quantum integrability, with a view towards theoretical high-energy physics
• Classical Liouville Three-point Functions from Riemann-Hilbert Analysis
• Solution of quantum integrable systems from quiver gauge theories