Argyres-Douglas theories, the Macdonald index, and an RG inequality
Here 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.
- 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:
- OSTI Identifier:
- Grant/Contract Number:
- SC0010008; SC0003883; SC0007897; SC0009924; PHY-1066293
- 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 1029-8479
- 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
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Supersymmetric gauge theory; Extended Supersymmetry; Conformal and W Symmetry; Renormalization Group
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