Implications of ANEC for SCFTs in four dimensions

Manenti, Andrea; Vichi, Alessandro; Stergiou, Andreas

doi:10.1007/JHEP01(2020)093

Title: Implications of ANEC for SCFTs in four dimensions

Journal Article · 16 January 2020 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/JHEP01(2020)093 · OSTI ID:1604034

Manenti, Andrea ^[1]; Vichi, Alessandro ^[1];

^[2]

Ecole Polytechnique Federale Lausanne (Switzlerland)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

We explore consequences of the Averaged Null Energy Condition (ANEC) for scaling dimensions Δ of operators in four-dimensional N = 1 superconformal field theories. We show that in many cases the ANEC bounds are stronger than the corresponding unitarity bounds on Δ. We analyze in detail chiral operators in the ($$\frac{1}{2}j$$,0) Lorentz representation and prove that the ANEC implies the lower bound Δ$$\frac{3}{2}j$$, which is stronger than the corresponding unitarity bound for j > 1. We also derive ANEC bounds on ($$\frac{1}{2}j$$,0) operators obeying other possible shortening conditions, as well as general ($$\frac{1}{2}j$$j,0) operators not obeying any shortening condition. In both cases we find that they are typically stronger than the corresponding unitarity bounds. Finally, we elucidate operator-dimension constraints that follow from our N = 1 results for multiplets of N = 2, 4 superconformal theories in four dimensions. By recasting the ANEC as a convex optimization problem and using standard semidefinite programming methods we are able to improve on previous analyses in the literature pertaining to the nonsupersymmetric case.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1604034

Report Number(s):: LA-UR--19-25902

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 1 Vol. 2020; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

References (42)

N=1 Superconformal Symmetry in Four-Dimensional Quantum Field Theory Osborn, Hugh Annals of Physics, Vol. 272, Issue 2 https://doi.org/10.1006/aphy.1998.5893	journal	March 1999
Representations of conformal supersymmetry Flato, Mosh�; Fronsdal, Christian Letters in Mathematical Physics, Vol. 8, Issue 2 https://doi.org/10.1007/BF00406399	journal	March 1984
All unitary ray representations of the conformal group SU(2,2) with positive energy Mack, G. Communications in Mathematical Physics, Vol. 55, Issue 1 https://doi.org/10.1007/BF01613145	journal	February 1977
General bootstrap equations in 4D CFTs Cuomo, Gabriel Francisco; Karateev, Denis; Kravchuk, Petr Journal of High Energy Physics, Vol. 2018, Issue 1 https://doi.org/10.1007/JHEP01(2018)130	journal	January 2018
Counting conformal correlators Kravchuk, Petr; Simmons-Duffin, David Journal of High Energy Physics, Vol. 2018, Issue 2 https://doi.org/10.1007/JHEP02(2018)096	journal	February 2018
Universal bounds on operator dimensions from the average null energy condition Córdova, Clay; Diab, Kenan Journal of High Energy Physics, Vol. 2018, Issue 2 https://doi.org/10.1007/JHEP02(2018)131	journal	February 2018
Constraining conformal field theories with a higher spin symmetry in d > 3 dimensions Alba, Vasyl; Diab, Kenan Journal of High Energy Physics, Vol. 2016, Issue 3 https://doi.org/10.1007/JHEP03(2016)044	journal	March 2016
Multiplets of superconformal symmetry in diverse dimensions Córdova, Clay; Dumitrescu, Thomas T.; Intriligator, Kenneth Journal of High Energy Physics, Vol. 2019, Issue 3 https://doi.org/10.1007/JHEP03(2019)163	journal	March 2019
On conformal field theories with extremal $ \frac{a}{c} $ values Zhiboedov, Alexander Journal of High Energy Physics, Vol. 2014, Issue 4 https://doi.org/10.1007/JHEP04(2014)038	journal	April 2014
A semidefinite program solver for the conformal bootstrap Simmons-Duffin, David Journal of High Energy Physics, Vol. 2015, Issue 6 https://doi.org/10.1007/JHEP06(2015)174	journal	June 2015
Fermion conformal bootstrap in 4d Karateev, Denis; Kravchuk, Petr; Serone, Marco Journal of High Energy Physics, Vol. 2019, Issue 6 https://doi.org/10.1007/JHEP06(2019)088	journal	June 2019
Comments on supercurrent multiplets, supersymmetric field theories and supergravity Komargodski, Zohar; Seiberg, Nathan Journal of High Energy Physics, Vol. 2010, Issue 7 https://doi.org/10.1007/JHEP07(2010)017	journal	July 2010
Averaged null energy condition from causality Hartman, Thomas; Kundu, Sandipan; Tajdini, Amirhossein Journal of High Energy Physics, Vol. 2017, Issue 7 https://doi.org/10.1007/JHEP07(2017)066	journal	July 2017
Higher spin ANEC and the space of CFTs Meltzer, David Journal of High Energy Physics, Vol. 2019, Issue 7 https://doi.org/10.1007/JHEP07(2019)001	journal	July 2019
Modular Hamiltonians for deformed half-spaces and the averaged null energy condition Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar Journal of High Energy Physics, Vol. 2016, Issue 9 https://doi.org/10.1007/JHEP09(2016)038	journal	September 2016
Two-point functions of conformal primary operators in N $$ \mathcal{N} $$ = 1 superconformal theories Li, Daliang; Stergiou, Andreas Journal of High Energy Physics, Vol. 2014, Issue 10 https://doi.org/10.1007/JHEP10(2014)037	journal	October 2014
Bounds on OPE coefficients from interference effects in the conformal collider Córdova, Clay; Maldacena, Juan; Turiaci, Gustavo J. Journal of High Energy Physics, Vol. 2017, Issue 11 https://doi.org/10.1007/JHEP11(2017)032	journal	November 2017
Light-ray operators in conformal field theory Kravchuk, Petr; Simmons-Duffin, David Journal of High Energy Physics, Vol. 2018, Issue 11 https://doi.org/10.1007/JHEP11(2018)102	journal	November 2018
Constraints on chiral operators in N = 2 $$ \mathcal{N}=2 $$ SCFTs Buican, Matthew; Nishinaka, Takahiro; Papageorgakis, Constantinos Journal of High Energy Physics, Vol. 2014, Issue 12 https://doi.org/10.1007/JHEP12(2014)095	journal	December 2014
R-current three-point functions in 4d N$$ \mathcal{N} $$ = 1 superconformal theories Manenti, Andrea; Stergiou, Andreas; Vichi, Alessandro Journal of High Energy Physics, Vol. 2018, Issue 12 https://doi.org/10.1007/JHEP12(2018)108	journal	December 2018
Matrix Sum-of-Squares Relaxations for Robust Semi-Definite Programs Scherer, C. W.; Hol, C. W. J. Mathematical Programming, Vol. 107, Issue 1-2 https://doi.org/10.1007/s10107-005-0684-2	journal	December 2005
All positive energy unitary irreducible representations of extended conformal supersymmetry Dobrev, V. K.; Petkova, V. B. Physics Letters B, Vol. 162, Issue 1-3 https://doi.org/10.1016/0370-2693(85)91073-1	journal	November 1985
Transformation properties of the supercurrent Ferrara, S.; Zumino, B. Nuclear Physics B, Vol. 87, Issue 2 https://doi.org/10.1016/0550-3213(75)90063-2	journal	March 1975
On short and semi-short representations for four-dimensional superconformal symmetry Dolan, F. A.; Osborn, H. Annals of Physics, Vol. 307, Issue 1 https://doi.org/10.1016/S0003-4916(03)00074-5	journal	September 2003
Comments on unparticles Grinstein, Benjamin; Intriligator, Kenneth; Rothstein, Ira Z. Physics Letters B, Vol. 662, Issue 4 https://doi.org/10.1016/j.physletb.2008.03.020	journal	May 2008
Correlation functions of conserved currents in calN = 2 superconformal theory Kuzenko, Sergei M.; Theisen, Stefan Classical and Quantum Gravity, Vol. 17, Issue 3 https://doi.org/10.1088/0264-9381/17/3/307	journal	January 2000
Chiral Rings and Anomalies in Supersymmetric Gauge Theory Cachazo, Freddy; Douglas, Michael R.; Seiberg, Nathan Journal of High Energy Physics, Vol. 2002, Issue 12 https://doi.org/10.1088/1126-6708/2002/12/071	journal	December 2002
Conformal collider physics: energy and charge correlations Hofman, Diego M.; Maldacena, Juan Journal of High Energy Physics, Vol. 2008, Issue 05 https://doi.org/10.1088/1126-6708/2008/05/012	journal	May 2008
Spectrum of type IIB supergravity on AdS 5 × T 11 : Predictions on N = 1 SCFT ’ s Ceresole, Anna; Dall’Agata, Gianguido; D’Auria, Riccardo Physical Review D, Vol. 61, Issue 6 https://doi.org/10.1103/PhysRevD.61.066001	journal	February 2000
N=1 Superconformal Symmetry in four Dimensions Park, Jeong-Hyuck International Journal of Modern Physics A, Vol. 13, Issue 11 https://doi.org/10.1142/S0217751X98000755	journal	April 1998
All unitary ray representations of the conformal group SU(2,2) with positive energy Mack, Gerhard Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2017-11746	text	January 1975
Restrictions imposed by superconformal invariance on quantum field theories Minwalla, Shiraz Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 4 https://doi.org/10.4310/ATMP.1998.v2.n4.a4	journal	January 1998
Comments on Unparticles Grinstein, Benjamin; Intriligator, Kenneth; Rothstein, Ira Z. arXiv https://doi.org/10.48550/arxiv.0801.1140	text	January 2008
Constraining conformal field theories with a higher spin symmetry in d> 3 dimensions Alba, Vasyl; Diab, Kenan arXiv https://doi.org/10.48550/arxiv.1510.02535	text	January 2015
Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar arXiv https://doi.org/10.48550/arxiv.1605.08072	text	January 2016
Counting Conformal Correlators Kravchuk, Petr; Simmons-Duffin, David arXiv https://doi.org/10.48550/arxiv.1612.08987	preprint	January 2016
Universal Bounds on Operator Dimensions from the Average Null Energy Condition Cordova, Clay; Diab, Kenan arXiv https://doi.org/10.48550/arxiv.1712.01089	text	January 2017
Light-ray operators in conformal field theory Kravchuk, Petr; Simmons-Duffin, David arXiv https://doi.org/10.48550/arxiv.1805.00098	text	January 2018
On Short and Semi-Short Representations for Four Dimensional Superconformal Symmetry Dolan, F. A.; Osborn, H. arXiv https://doi.org/10.48550/arxiv.hep-th/0209056	text	January 2002
N=1 Superconformal Symmetry in Four Dimensions Park, Jeong-Hyuck arXiv https://doi.org/10.48550/arxiv.hep-th/9703191	text	January 1997
Restrictions Imposed by Superconformal Invariance on Quantum Field Theories Minwalla, Shiraz arXiv https://doi.org/10.48550/arxiv.hep-th/9712074	text	January 1997
N=1 Superconformal Symmetry in Four Dimensional Quantum Field Theory Osborn, Hugh arXiv https://doi.org/10.48550/arxiv.hep-th/9808041	text	January 1998

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