Implications of ANEC for SCFTs in four dimensions
Abstract
We explore consequences of the Averaged Null Energy Condition (ANEC) for scaling dimensions Δ of operators in fourdimensional 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 operatordimension 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.
 Authors:

 Ecole Polytechnique Federale Lausanne (Switzlerland)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE Laboratory Directed Research and Development (LDRD) Program
 OSTI Identifier:
 1604034
 Report Number(s):
 LAUR1925902
Journal ID: ISSN 10298479; TRN: US2104184
 Grant/Contract Number:
 89233218CNA000001
 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: 2020; Journal Issue: 1; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Atomic; Nuclear and Particle Physics
Citation Formats
Manenti, Andrea, Vichi, Alessandro, and Stergiou, Andreas. Implications of ANEC for SCFTs in four dimensions. United States: N. p., 2020.
Web. https://doi.org/10.1007/JHEP01(2020)093.
Manenti, Andrea, Vichi, Alessandro, & Stergiou, Andreas. Implications of ANEC for SCFTs in four dimensions. United States. https://doi.org/10.1007/JHEP01(2020)093
Manenti, Andrea, Vichi, Alessandro, and Stergiou, Andreas. Thu .
"Implications of ANEC for SCFTs in four dimensions". United States. https://doi.org/10.1007/JHEP01(2020)093. https://www.osti.gov/servlets/purl/1604034.
@article{osti_1604034,
title = {Implications of ANEC for SCFTs in four dimensions},
author = {Manenti, Andrea and Vichi, Alessandro and Stergiou, Andreas},
abstractNote = {We explore consequences of the Averaged Null Energy Condition (ANEC) for scaling dimensions Δ of operators in fourdimensional 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 operatordimension 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.},
doi = {10.1007/JHEP01(2020)093},
journal = {Journal of High Energy Physics (Online)},
number = 1,
volume = 2020,
place = {United States},
year = {2020},
month = {1}
}
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