On the integrability of four dimensional \( \mathcal{N}=2 \) gauge theories in the omega background. (English) Zbl 1342.83342
Summary: We continue to investigate the relationship between the infrared physics of \(\mathcal N = 2\) 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 \(\mathcal N = 2\) 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.
MSC:
| 83E30 | String and superstring theories in gravitational theory |
Keywords:
supersymmetric gauge theory; extended supersymmetry; integrable field theories; string dualityReferences:
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