Gauge Theories and Macdonald Polynomials

Details Gauge Theories and Macdonald Polynomials Gauge Theories and Macdonald Polynomials

2011-10-17

arxiv.org/abs/1110.3740v2

Physics

High Energy Physics

High Energy Physics - Theory

57 pages, 6 figures, v2: references added and minor improvements

Scientific paper

We study the 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 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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