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Title: Universal bounds on operator dimensions from the average null energy condition

We show that the average null energy condition implies novel lower bounds on the scaling dimensions of highly-chiral primary operators in four-dimensional 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:
 [1] ; ORCiD logo [2]
  1. Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
  2. Princeton Univ., NJ (United States). Dept. of Physics
Publication Date:
Grant/Contract Number:
SC0009988
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 1029-8479
Publisher:
Springer Berlin
Research Org:
Inst. for Advanced Study, Princeton, NJ (United States)
Sponsoring Org:
USDOE Office of Science (SC)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal Field Theory; Higher Spin Symmetry
OSTI Identifier:
1502475

Córdova, Clay, and Diab, Kenan. Universal bounds on operator dimensions from the average null energy condition. United States: N. p., Web. doi:10.1007/jhep02(2018)131.
Córdova, Clay, & Diab, Kenan. Universal bounds on operator dimensions from the average null energy condition. United States. doi:10.1007/jhep02(2018)131.
Córdova, Clay, and Diab, Kenan. 2018. "Universal bounds on operator dimensions from the average null energy condition". United States. doi: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 highly-chiral primary operators in four-dimensional 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}
}