Macdonald index and chiral algebra

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For any 4d N = 2 SCFT, there is a subsector described by a 2d chiral algebra. The vacuum character of the chiral algebra reproduces the Schur index of the corresponding 4d theory. The Macdonald index counts the same set of operators as the Schur index, but the former has one more fugacity than the latter. We conjecture a prescription to obtain the Macdonald index from the chiral algebra. The vacuum module admits a filtration, from which we construct an associated graded vector space. From this grading, we conjecture a notion of re fined character for the vacuum module of a chiral algebra, which reproduces the Macdonald index. We test this prescription for the Argyres-Douglas theories of type (A(1); A(2n)) and (A(1); D2n+1) where the chiral algebras are given by Virasoro and su (2) affine Kac-Moody algebra. When the chiral algebra has more than one family of generators, our prescription requires a knowledge of the generators from the 4d.
Publisher
SPRINGER
Issue Date
2017-08
Language
English
Article Type
Article
Citation

JOURNAL OF HIGH ENERGY PHYSICS, no.8

ISSN
1029-8479
DOI
10.1007/JHEP08(2017)044
URI
http://hdl.handle.net/10203/274001
Appears in Collection
PH-Journal Papers(저널논문)
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