Universal bounds on operator dimensions from the average null energy condition
Abstract
We show that the average null energy condition implies novel lower bounds on the scaling dimensions of highlychiral primary operators in fourdimensional conformal field theories. Denoting the spin of an operator by a pair of integers ($$k\overline{k}\ $$) specifying the transformations under chiral su(2) rotations, we explicitly demonstrate these new bounds for operators transforming in (k, 0) and (k, 1) representations for sufficiently large k. Based on these calculations, along with intuition from free field theory, we conjecture that in any unitary conformal field theory, primary local operators of spin ($$k\overline{k}\ $$) and scaling dimension Δ satisfy Δ ≥ max{$$k\overline{k}\ $$}. If $$k\overline{k}\ $$ > 4 , this is stronger than the unitarity bound.
 Authors:

 Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
 Princeton Univ., NJ (United States). Dept. of Physics
 Publication Date:
 Research Org.:
 Institute for Advanced Study, Princeton, NJ (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC)
 OSTI Identifier:
 1502475
 Grant/Contract Number:
 SC0009988
 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: 2018; Journal Issue: 2; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal Field Theory; Higher Spin Symmetry
Citation Formats
Córdova, Clay, and Diab, Kenan. Universal bounds on operator dimensions from the average null energy condition. United States: N. p., 2018.
Web. doi:10.1007/jhep02(2018)131.
Córdova, Clay, & Diab, Kenan. Universal bounds on operator dimensions from the average null energy condition. United States. https://doi.org/10.1007/jhep02(2018)131
Córdova, Clay, and Diab, Kenan. Wed .
"Universal bounds on operator dimensions from the average null energy condition". United States. https://doi.org/10.1007/jhep02(2018)131. https://www.osti.gov/servlets/purl/1502475.
@article{osti_1502475,
title = {Universal bounds on operator dimensions from the average null energy condition},
author = {Córdova, Clay and Diab, Kenan},
abstractNote = {We show that the average null energy condition implies novel lower bounds on the scaling dimensions of highlychiral primary operators in fourdimensional conformal field theories. Denoting the spin of an operator by a pair of integers ($k\overline{k}\ $) specifying the transformations under chiral su(2) rotations, we explicitly demonstrate these new bounds for operators transforming in (k, 0) and (k, 1) representations for sufficiently large k. Based on these calculations, along with intuition from free field theory, we conjecture that in any unitary conformal field theory, primary local operators of spin ($k\overline{k}\ $) and scaling dimension Δ satisfy Δ ≥ max{$k\overline{k}\ $}. If $k\overline{k}\ $ > 4 , this is stronger than the unitarity bound.},
doi = {10.1007/jhep02(2018)131},
journal = {Journal of High Energy Physics (Online)},
number = 2,
volume = 2018,
place = {United States},
year = {2018},
month = {2}
}
Web of Science
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