Communications in Mathematical Physics

, Volume 319, Issue 1, pp 147–193 | Cite as

Gauge Theories and Macdonald Polynomials

  • Abhijit Gadde
  • Leonardo RastelliEmail author
  • Shlomo S. Razamat
  • Wenbin Yan


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.


Gauge Theory Partition Function Vector Multiplet Young Diagram Coulomb Branch 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Abhijit Gadde
    • 1
    • 2
  • Leonardo Rastelli
    • 1
    Email author
  • Shlomo S. Razamat
    • 1
    • 3
  • Wenbin Yan
    • 1
  1. 1.C.N. Yang Institute for Theoretical Physics, State University of New York at Stony BrookStony BrookUSA
  2. 2.California Institute of TechnologyPasadenaUSA
  3. 3.Institute for Advanced StudyPrincetonUSA

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