Gauge Theories and Macdonald Polynomials

By Abhijit Gadde, L. Rastelli, Shlomo S. Razamat, Wenbin Yan. 2011

458 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/176cf7ce81b82b7a5c7bee9e85ac8e40d288ac02

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Citations in the corpus

N=1 theories of class S_k (2015, background): “It is reasonable to assume that the transformations can be “diagonalized”, as in the class S case [31, 32], by expanding the free trinion into “wavefunctions” associated to each puncture,”
On the superconformal index of Argyres–Douglas theories (2015, methodology): “Examples of such limits include both the Coulomb branch and Hall-Littlewood limits described in [16].”
Infinite Chiral Symmetry in Four Dimensions (2013, background): “There exist a variety of trace formulas [19, 21] that can be defined on the Hilbert space of an N = 2 SCFT such that the result receives contributions only from states that lie in short representations of the superconformal algebra, with the contributions being such that the indices are insensitive ”
General Argyres-Douglas theory (2012, background): “It is also interesting to calculate the superconformal index for these theories, see the results for the regular puncture case [70].”
Schur indices, BPS particles, and Argyres-Douglas theories (2015, background): “Specifically, from the character decompositions of [3, 43] one may deduce that if the theory in question does not contain any free sector and has rank nf flavor symmetry, then the first few terms in the Schur index (at vanishing flavor fugacity) take the form I(q) = 1 + (nf )q + (c3)q + (nf + 1 + c4”
2d index and surface operators (2013, methodology): “They are easily evaluated [11] by listing contributions of the letters with δ = 0 in table 3:”
N=1 Deformations and RG Flows of N=2 SCFTs (2016, methodology): “The Coulomb branch limit of the index [55] is obtained by taking p, q, t→ 0 while pq t = u fixed.”
Non-Lagrangian theories from brane junctions (2013, background): “In particular, it was pointed out that it coincides with the HallLittlewood limit of the superconformal index for particular values of the fugacities [88].”