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

TL;DR

This paper explores the deep connections between four-dimensional N=2 supersymmetric gauge theories and integrable models, revealing dualities, quantizations, and conformal field theory correspondences that enhance understanding of their infrared physics.

Contribution

It establishes dualities among integrable systems via different quantizations of the Seiberg-Witten curve and links conformal blocks of CFTs to integrable models in the context of N=2 gauge theories.

Findings

Proved dualities among integrable models like Gaudin, Calogero-Moser, and spin chains.

Identified equivalences between conformal blocks of Toda and WZNW theories.

Connected gauge theories with conformal field theories through AGT duality.

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.