Gauge Theories and Macdonald Polynomials

TL;DR

This paper explores the superconformal index of N=2 4D theories, proposing explicit formulas for A-type class S quivers, and reveals connections to deformed 2D Yang-Mills theory with Macdonald polynomials as key algebraic elements.

Contribution

It introduces conjectured explicit formulas for superconformal indices of A-type class S quivers lacking Lagrangian descriptions, linking them to 2D topological theories and Macdonald polynomials.

Findings

Proposed explicit formulas for superconformal indices of A-type class S quivers.

Identified the index as a correlator in a deformed 2D Yang-Mills theory.

Found that structure constants are diagonal in Macdonald polynomial basis.

Abstract

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.