ArgyresDouglas theories, the Macdonald index, and an RG inequality
Here we conjecture closedform expressions for the Macdonald limits of the superconformal indices of the (A _{1},A _{2n₋3}) and (A _{1},D _{2n}) ArgyresDouglas (AD) theories in terms of certain simple deformations of Macdonald polynomials. As checks of our conjectures, we demonstrate compatibility with two Sdualities, we show symmetry enhancement for special values of n, and we argue that our expressions encode a nontrivial 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 HallLittlewood 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 fourdimensional parent theories. Finally, we comment on the implications of our work for more general $N = 2$ superconformal field theories.
 Authors:

^{[1]};
^{[2]}
 Rutgers Univ., Piscataway, NJ (United States). NHETC and Dept. of Physics and Astronomy; Univ. of Chicago, IL (United States). Enrico Fermi Inst.
 Rutgers Univ., Piscataway, NJ (United States). NHETC and Dept. of Physics and Astronomy; Kyoto Univ. (Japan). Yukawa Inst. for Theoretical Physics
 Publication Date:
 Grant/Contract Number:
 SC0010008; SC0003883; SC0007897; SC0009924; PHY1066293
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 2; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Research Org:
 Rutgers Univ., Piscataway, NJ (United States); Univ. of Chicago, IL (United States)
 Sponsoring Org:
 USDOE Office of Science (SC); National Science Foundation (NSF)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Supersymmetric gauge theory; Extended Supersymmetry; Conformal and W Symmetry; Renormalization Group
 OSTI Identifier:
 1327220
Buican, Matthew, and Nishinaka, Takahiro. ArgyresDouglas theories, the Macdonald index, and an RG inequality. United States: N. p.,
Web. doi:10.1007/JHEP02(2016)159.
Buican, Matthew, & Nishinaka, Takahiro. ArgyresDouglas theories, the Macdonald index, and an RG inequality. United States. doi:10.1007/JHEP02(2016)159.
Buican, Matthew, and Nishinaka, Takahiro. 2016.
"ArgyresDouglas theories, the Macdonald index, and an RG inequality". United States.
doi:10.1007/JHEP02(2016)159. https://www.osti.gov/servlets/purl/1327220.
@article{osti_1327220,
title = {ArgyresDouglas theories, the Macdonald index, and an RG inequality},
author = {Buican, Matthew and Nishinaka, Takahiro},
abstractNote = {Here we conjecture closedform expressions for the Macdonald limits of the superconformal indices of the (A1,A2n₋3) and (A1,D2n) ArgyresDouglas (AD) theories in terms of certain simple deformations of Macdonald polynomials. As checks of our conjectures, we demonstrate compatibility with two Sdualities, we show symmetry enhancement for special values of n, and we argue that our expressions encode a nontrivial 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 HallLittlewood limits of our indices are equivalent to the corresponding Higgs branch Hilbert series. We explain this fact by considering the S1 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 fourdimensional parent theories. Finally, we comment on the implications of our work for more general $N = 2$ superconformal field theories.},
doi = {10.1007/JHEP02(2016)159},
journal = {Journal of High Energy Physics (Online)},
number = 2,
volume = 2016,
place = {United States},
year = {2016},
month = {2}
}