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Title: Argyres-Douglas theories, the Macdonald index, and an RG inequality

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2]
  1. Rutgers Univ., Piscataway, NJ (United States). NHETC and Dept. of Physics and Astronomy; Univ. of Chicago, IL (United States). Enrico Fermi Inst.
  2. Rutgers Univ., Piscataway, NJ (United States). NHETC and Dept. of Physics and Astronomy; Kyoto Univ. (Japan). Yukawa Inst. for Theoretical Physics
+ Show Author Affiliations

Here we conjecture closed-form expressions for the Macdonald limits of the superconformal indices of the (A1,A2n₋3) and (A1,D2n) 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 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 four-dimensional parent theories. Finally, we comment on the implications of our work for more general $N = 2$ superconformal field theories.

Research Organization:
Rutgers Univ., Piscataway, NJ (United States); Univ. of Chicago, IL (United States)
Sponsoring Organization:
USDOE Office of Science (SC); National Science Foundation (NSF)
Grant/Contract Number:
SC0010008; SC0003883; SC0007897; SC0009924; PHY-1066293
OSTI ID:
1327220
Journal Information:
Journal of High Energy Physics (Online), Vol. 2016, Issue 2; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 43 works
Citation information provided by
Web of Science

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Cited By (7)

On the chiral algebra of Argyres-Douglas theories and S-duality journal April 2018
Conformal manifolds in four dimensions and chiral algebras journal October 2016
Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories journal February 2018
Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory text January 2017
Enhancement of Supersymmetry via Renormalization Group Flow and the Superconformal Index text January 2016
Surface Defects and Chiral Algebras text January 2017
Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory text January 2017

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Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Supersymmetric gauge theory
Extended Supersymmetry
Conformal and W Symmetry
Renormalization Group