Macdonald index and chiral algebra
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 (A _{1}, A _{2n}) and (A _{1}, D _{2n+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.
- Publication Date:
- Grant/Contract Number:
- sc0009919
- 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
- Research Org:
- Univ. of California, San Diego, CA (United States)
- Sponsoring Org:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); Korea Institute for Advanced Study (KIAS), Seoul (South Korea); Stony Brook Univ., NY (United States). Simons Center for Geometry and Physics
- 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
- OSTI Identifier:
- 1423950
Song, Jaewon. Macdonald index and chiral algebra. United States: N. p.,
Web. doi:10.1007/JHEP08(2017)044.
Song, Jaewon. Macdonald index and chiral algebra. United States. doi:10.1007/JHEP08(2017)044.
Song, Jaewon. 2017.
"Macdonald index and chiral algebra". United States.
doi: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}
}