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Title: 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 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.

Authors:
 [1];  [1]; ORCiD logo [2]
+ Show Author Affiliations
  1. Ecole Polytechnique Federale Lausanne (Switzlerland)
  2. 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):
LA-UR-19-25902
Journal ID: ISSN 1029-8479; 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 1029-8479
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. doi:10.1007/JHEP01(2020)093.
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Manenti, Andrea, Vichi, Alessandro, & Stergiou, Andreas. Implications of ANEC for SCFTs in four dimensions. United States. https://doi.org/10.1007/JHEP01(2020)093
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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.
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@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 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.},
doi = {10.1007/JHEP01(2020)093},
journal = {Journal of High Energy Physics (Online)},
number = 1,
volume = 2020,
place = {United States},
year = {Thu Jan 16 00:00:00 EST 2020},
month = {Thu Jan 16 00:00:00 EST 2020}
}
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https://doi.org/10.1007/JHEP01(2020)093
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