{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/implications-of-anec-for-scfts-in-four","title":"Implications of ANEC for SCFTs in four dimensions","arxiv_id":"1905.09293","date":"2019-05-22","proceeding":null,"authors":["Andrea Manenti","Andreas Stergiou","Alessandro Vichi"],"abstract":"We explore consequences of the Averaged Null Energy Condition (ANEC) for scaling dimensions $\\Delta$ of operators in four-dimensional $\\mathcal{N}=1$ superconformal field theories. We show that in many cases the ANEC bounds are stronger than the corresponding unitarity bounds on $\\Delta$. We analyze in detail chiral operators in the $(\\frac12 j,0)$ Lorentz representation and prove that the ANEC implies the lower bound $\\Delta\\ge\\frac32j$, which is stronger than the corresponding unitarity bound for $j>1$. We also derive ANEC bounds on $(\\frac12 j,0)$ operators obeying other possible shortening conditions, as well as general $(\\frac12 j,0)$ 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 $\\mathcal{N}=1$ results for multiplets of $\\mathcal{N}=2,4$ 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.","url_abs":"http://arxiv.org/abs/1905.09293v1","url_pdf":"http://arxiv.org/pdf/1905.09293v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"implications-of-anec-for-scfts-in-four","repo_url":"https://gitlab.com/maneandrea/spinoralgebra","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}