Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 2, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP02(2016)159
Keywords
Supersymmetric gauge theory; Extended Supersymmetry; Conformal and W Symmetry; Renormalization Group
Categories
Funding
- National Science Foundation [PHY-1066293]
- Simons Center for Geometry and Physics, Stony Brook University
- U.S. Department of Energy [DOE-SC0010008, DOE-ARRA-SC0003883, DOE-DE-SC0007897, DE-SC0009924]
- Yukawa Memorial Foundation
- U.S. Department of Energy (DOE) [DE-SC0009924] Funding Source: U.S. Department of Energy (DOE)
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We conjecture closed-form expressions for the Macdonald limits of the superconformal indices of the (A(1), A(2n-3)) and (A(1), D-2n) Argyres-Douglas (AD) theories in terms of certain simple deformations of Macdonald polynomials. As checks of our conjectures, we demonstrate compatibility with two S-dualities, we show symmetry enhancement for special values of n, and we argue that our expressions encode a non-trivial set of renormalization group flows. Moreover, we demonstrate that, for certain values of n, our conjectures imply simple operator relations involving composites built out of the SU(2)(R) currents and flavor symmetry moment maps, and we find a consistent picture in which these relations give rise to certain null states in the corresponding chiral algebras. In addition, we show that the Hall-Littlewood limits of our indices are equivalent to the corresponding Higgs branch Hilbert series. We explain this fact by considering the S-1 reductions of our theories and showing that the equivalence follows from an inequality on monopole quantum numbers whose coefficients are fixed by data of the four-dimensional parent theories. Finally, we comment on the implications of our work for more general N = 2 superconformal field theories.
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