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Gauge Theories and Macdonald Polynomials

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Abstract

We study the \({\mathcal{N}=2}\) four-dimensional superconformal index in various interesting limits, such that only states annihilated by more than one supercharge contribute. Extrapolating from the SU(2) generalized quivers, which have a Lagrangian description, we conjecture explicit formulae for all A-type quivers of class \({\mathcal S}\), which in general do not have one. We test our proposals against several expected dualities. The index can always be interpreted as a correlator in a two-dimensional topological theory, which we identify in each limit as a certain deformation of two-dimensional Yang-Mills theory. The structure constants of the topological algebra are diagonal in the basis of Macdonald polynomials of the holonomies.

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Authors and Affiliations

  1. C.N. Yang Institute for Theoretical Physics, State University of New York at Stony Brook, Stony Brook, NY, 11794-3840, USA

    Abhijit Gadde, Leonardo Rastelli, Shlomo S. Razamat & Wenbin Yan

  2. California Institute of Technology, Pasadena, CA, 91125, USA

    Abhijit Gadde

  3. Institute for Advanced Study, Princeton, NJ, 08540, USA

    Shlomo S. Razamat

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  1. Abhijit Gadde
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  2. Leonardo Rastelli
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  3. Shlomo S. Razamat
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  4. Wenbin Yan
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Correspondence to Leonardo Rastelli.

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Communicated by N. A. Nekrasov

In memory of Francis A. Dolan

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Gadde, A., Rastelli, L., Razamat, S.S. et al. Gauge Theories and Macdonald Polynomials. Commun. Math. Phys. 319, 147–193 (2013). https://doi.org/10.1007/s00220-012-1607-8

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