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Title: Macdonald index and chiral algebra

Abstract

For any 4dN = 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. Here, 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 refined 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 (A1, A2n) and (A1, D2n+1) where the chiral algebras are given by Virasoro and $$ˆ\atop{su}$$(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.

Authors:
 [1]
  1. Univ. of California San Diego, La Jolla, CA (United States). Dept. of Physics
Publication Date:
Research Org.:
Univ. of California, San Diego, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); Korea Institute for Advanced Study (KIAS), Seoul (South Korea); Stony Brook Univ., NY (United States). Simons Center for Geometry and Physics
OSTI Identifier:
1423950
Grant/Contract Number:  
sc0009919
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 8; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Conformal and W Symmetry; Conformal Field Theory; Extended Supersymmetry; Supersymmetric Gauge Theory

Citation Formats

Song, Jaewon. Macdonald index and chiral algebra. United States: N. p., 2017. Web. https://doi.org/10.1007/JHEP08(2017)044.
Song, Jaewon. Macdonald index and chiral algebra. United States. https://doi.org/10.1007/JHEP08(2017)044
Song, Jaewon. Thu . "Macdonald index and chiral algebra". United States. https://doi.org/10.1007/JHEP08(2017)044. https://www.osti.gov/servlets/purl/1423950.
@article{osti_1423950,
title = {Macdonald index and chiral algebra},
author = {Song, Jaewon},
abstractNote = {For any 4dN = 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. Here, 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 refined 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 (A1, A2n) and (A1, D2n+1) where the chiral algebras are given by Virasoro and $ˆ\atop{su}$(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.},
doi = {10.1007/JHEP08(2017)044},
journal = {Journal of High Energy Physics (Online)},
number = 8,
volume = 2017,
place = {United States},
year = {2017},
month = {8}
}

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Cited by: 13 works
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    Works referencing / citing this record:

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