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On the integrability of four dimensional \( \mathcal{N}=2 \) gauge theories in the omega background

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Abstract

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.

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Authors and Affiliations

  1. Department of Physics and Center for Theoretical Sciences, National Taiwan University, Taipei, 10617, Taiwan

    Heng-Yu Chen & Po-Shen Hsin

  2. School of Physics and Astronomy, University of Minnesota, 116 Church Street S.E., Minneapolis, MN, 55455, U.S.A.

    Peter Koroteev

  3. Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON, N2L2Y5, Canada

    Peter Koroteev

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  1. Heng-Yu Chen
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  2. Po-Shen Hsin
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ArXiv ePrint: 1305.5614

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Chen, HY., Hsin, PS. & Koroteev, P. On the integrability of four dimensional \( \mathcal{N}=2 \) gauge theories in the omega background. J. High Energ. Phys. 2013, 76 (2013). https://doi.org/10.1007/JHEP08(2013)076

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