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. https://doi.org/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
Figures / Tables:
Works referenced in this record:
Topological censorship
journal, September 1993
 Friedman, John L.; Schleich, Kristin; Witt, Donald M.
 Physical Review Letters, Vol. 71, Issue 10
Constraints on parity violating conformal field theories in d = 3
journal, November 2017
 Chowdhury, Subham Dutta; David, Justin R.; Prakash, Shiroman
 Journal of High Energy Physics, Vol. 2017, Issue 11
Constraining conformal field theories with a higher spin symmetry in d > 3 dimensions
journal, March 2016
 Alba, Vasyl; Diab, Kenan
 Journal of High Energy Physics, Vol. 2016, Issue 3
On superconformal characters and partition functions in three dimensions
journal, February 2010
 Dolan, F. A.
 Journal of Mathematical Physics, Vol. 51, Issue 2
Limits on massless particles
journal, October 1980
 Weinberg, Steven; Witten, Edward
 Physics Letters B, Vol. 96, Issue 12
Aspects of superconformal multiplets in D > 4
journal, November 2016
 Buican, Matthew; Hayling, Joseph; Papageorgakis, Constantinos
 Journal of High Energy Physics, Vol. 2016, Issue 11
Averaged null energy condition from causality
journal, July 2017
 Hartman, Thomas; Kundu, Sandipan; Tajdini, Amirhossein
 Journal of High Energy Physics, Vol. 2017, Issue 7
Higher derivative gravity, causality and positivity of energy in a UV complete QFT
journal, December 2009
 Hofman, Diego M.
 Nuclear Physics B, Vol. 823, Issue 12
AdS7/CFT6, GaussBonnet gravity, and viscosity bound
journal, March 2010
 de Boer, Jan; Kulaxizi, Manuela; Parnachev, Andrei
 Journal of High Energy Physics, Vol. 2010, Issue 3
Kontravariante Formen auf induzierten Darstellungen halbeinfacher LieAlgebren
journal, February 1977
 Jantzen, Jens C.
 Mathematische Annalen, Vol. 226, Issue 1
Spectral sum rules for conformal field theories in arbitrary dimensions
journal, July 2017
 Chowdhury, Subham Dutta; David, Justin R.; Prakash, Shiroman
 Journal of High Energy Physics, Vol. 2017, Issue 7
Spinning conformal correlators
journal, November 2011
 Costa, Miguel S.; Penedones, João; Poland, David
 Journal of High Energy Physics, Vol. 2011, Issue 11
Nonpositivity of the energy density in quantized field theories
journal, April 1965
 Epstein, H.; Glaser, V.; Jaffe, A.
 Il Nuovo Cimento, Vol. 36, Issue 3
Restrictions imposed by superconformal invariance on quantum field theories
journal, January 1998
 Minwalla, Shiraz
 Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 4
General bootstrap equations in 4D CFTs
journal, January 2018
 Cuomo, Gabriel Francisco; Karateev, Denis; Kravchuk, Petr
 Journal of High Energy Physics, Vol. 2018, Issue 1
A proof of the conformal collider bounds
journal, June 2016
 Hofman, Diego M.; Li, Daliang; Meltzer, David
 Journal of High Energy Physics, Vol. 2016, Issue 6
Modular Hamiltonians for deformed halfspaces and the averaged null energy condition
journal, September 2016
 Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar
 Journal of High Energy Physics, Vol. 2016, Issue 9
Implications of Conformal Invariance in Field Theories for General Dimensions
journal, May 1994
 Osborn, H.; Petkou, A.
 Annals of Physics, Vol. 231, Issue 2
All unitary ray representations of the conformal group SU(2,2) with positive energy
journal, February 1977
 Mack, G.
 Communications in Mathematical Physics, Vol. 55, Issue 1
On conformal field theories with extremal $ \frac{a}{c} $ values
journal, April 2014
 Zhiboedov, Alexander
 Journal of High Energy Physics, Vol. 2014, Issue 4
Counting conformal correlators
journal, February 2018
 Kravchuk, Petr; SimmonsDuffin, David
 Journal of High Energy Physics, Vol. 2018, Issue 2
Twopoint functions of conformal primary operators in N $$ \mathcal{N} $$ = 1 superconformal theories
journal, October 2014
 Li, Daliang; Stergiou, Andreas
 Journal of High Energy Physics, Vol. 2014, Issue 10
Conformal collider physics: energy and charge correlations
journal, May 2008
 Hofman, Diego M.; Maldacena, Juan
 Journal of High Energy Physics, Vol. 2008, Issue 05
On short and semishort representations for fourdimensional superconformal symmetry
journal, September 2003
 Dolan, F. A.; Osborn, H.
 Annals of Physics, Vol. 307, Issue 1
Holographic GB gravity in arbitrary dimensions
journal, March 2010
 Buchel, Alex; Escobedo, Jorge; Myers, Robert C.
 Journal of High Energy Physics, Vol. 2010, Issue 3
General threepoint functions in 4D CFT
journal, January 2015
 Elkhidir, Emtinan; Karateev, Denis; Serone, Marco
 Journal of High Energy Physics, Vol. 2015, Issue 1
Bounds on OPE coefficients from interference effects in the conformal collider
journal, November 2017
 Córdova, Clay; Maldacena, Juan; Turiaci, Gustavo J.
 Journal of High Energy Physics, Vol. 2017, Issue 11
All unitary ray representations of the conformal group SU(2,2) with positive energy
text, January 1975
 Mack, Gerhard
 Deutsches ElektronenSynchrotron, DESY, Hamburg
Works referencing / citing this record:
Implications of ANEC for SCFTs in four dimensions
journal, January 2020
 Manenti, Andrea; Stergiou, Andreas; Vichi, Alessandro
 Journal of High Energy Physics, Vol. 2020, Issue 1
Exploring 2group global symmetries
journal, February 2019
 Córdova, Clay; Dumitrescu, Thomas T.; Intriligator, Kenneth
 Journal of High Energy Physics, Vol. 2019, Issue 2
Higher spin ANEC and the space of CFTs
journal, July 2019
 Meltzer, David
 Journal of High Energy Physics, Vol. 2019, Issue 7
Correlators of mixed symmetry operators in defect CFTs
journal, October 2018
 Guha, Sunny; Nagaraj, Balakrishnan
 Journal of High Energy Physics, Vol. 2018, Issue 10
Lightray operators in conformal field theory
journal, November 2018
 Kravchuk, Petr; SimmonsDuffin, David
 Journal of High Energy Physics, Vol. 2018, Issue 11
The conformal bootstrap: Theory, numerical techniques, and applications
journal, January 2019
 Poland, David; Rychkov, Slava; Vichi, Alessandro
 Reviews of Modern Physics, Vol. 91, Issue 1
Figures / Tables found in this record: