On superconformal characters and partition functions in three dimensions
Abstract
Possible short and semishort positive energy, unitary representations of the Osp(2N4) superconformal group in three dimensions are discussed. Corresponding character formulas are obtained, consistent with character formulas for the SO(3,2) conformal group, revealing long multiplet decomposition at unitarity bounds in a simple way. Limits, corresponding to reduction to various Osp(2N4) subalgebras, are taken in the characters that isolate contributions from fewer states, at a given unitarity threshold, leading to considerably simpler formula. Via these limits, applied to partition functions, closed formula for the generating functions for numbers of BPS operators in the free field limit of superconformal U(n)xU(n) N=6 ChernSimons theory and its supergravity dual are obtained in the large n limit. Partial counting of semishort operators is performed and consistency between operator counting for the free field and supergravity limits with long multiplet decomposition rules is explicitly demonstrated. Partition functions counting certain protected scalar primary semishort operators, and their superconformal descendants, are proposed and computed for large n. Certain chiral ring partition functions are discussed from a combinatorial perspective.
 Authors:

 Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands)
 Publication Date:
 OSTI Identifier:
 21335908
 Resource Type:
 Journal Article
 Journal Name:
 Journal of Mathematical Physics
 Additional Journal Information:
 Journal Volume: 51; Journal Issue: 2; Other Information: DOI: 10.1063/1.3211091; (c) 2010 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 00222488
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CHIRALITY; CONFORMAL GROUPS; CONFORMAL INVARIANCE; PARTITION FUNCTIONS; QUANTUM FIELD THEORY; SO2 GROUPS; SO3 GROUPS; SUPERGRAVITY; UNITARITY
Citation Formats
Dolan, F A. On superconformal characters and partition functions in three dimensions. United States: N. p., 2010.
Web. doi:10.1063/1.3211091.
Dolan, F A. On superconformal characters and partition functions in three dimensions. United States. https://doi.org/10.1063/1.3211091
Dolan, F A. 2010.
"On superconformal characters and partition functions in three dimensions". United States. https://doi.org/10.1063/1.3211091.
@article{osti_21335908,
title = {On superconformal characters and partition functions in three dimensions},
author = {Dolan, F A},
abstractNote = {Possible short and semishort positive energy, unitary representations of the Osp(2N4) superconformal group in three dimensions are discussed. Corresponding character formulas are obtained, consistent with character formulas for the SO(3,2) conformal group, revealing long multiplet decomposition at unitarity bounds in a simple way. Limits, corresponding to reduction to various Osp(2N4) subalgebras, are taken in the characters that isolate contributions from fewer states, at a given unitarity threshold, leading to considerably simpler formula. Via these limits, applied to partition functions, closed formula for the generating functions for numbers of BPS operators in the free field limit of superconformal U(n)xU(n) N=6 ChernSimons theory and its supergravity dual are obtained in the large n limit. Partial counting of semishort operators is performed and consistency between operator counting for the free field and supergravity limits with long multiplet decomposition rules is explicitly demonstrated. Partition functions counting certain protected scalar primary semishort operators, and their superconformal descendants, are proposed and computed for large n. Certain chiral ring partition functions are discussed from a combinatorial perspective.},
doi = {10.1063/1.3211091},
url = {https://www.osti.gov/biblio/21335908},
journal = {Journal of Mathematical Physics},
issn = {00222488},
number = 2,
volume = 51,
place = {United States},
year = {2010},
month = {2}
}