{"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/higher-operations-in-perturbation-theory","title":"Higher Operations in Perturbation Theory","arxiv_id":"2403.13049","date":"2024-03-19","proceeding":null,"authors":["Davide Gaiotto","Justin Kulp","Jingxiang Wu"],"abstract":"We discuss the role of formal deformation theory in quantum field theories and present various ``higher operations'' which control their deformations, (generalized) OPEs, and anomalies. Particular attention is paid to holomorphic-topological theories where we systematically describe and regularize the Feynman diagrams which compute these higher operations in free and perturbative scenarios, including examples with defects. We prove geometrically that the resulting higher operations satisfy expected ``quadratic axioms,'' which can be interpreted physically as a form of Wess-Zumino consistency condition for BRST symmetry. We discuss a higher-dimensional analogue of Kontsevich's formality theorem, which proves the absence of perturbative corrections in TQFTs with two or more topological directions. We discuss at some length the relation of our work to the theory of factorization algebras and provide an introduction to the subject for physicists.","url_abs":"https://arxiv.org/abs/2403.13049v1","url_pdf":"https://arxiv.org/pdf/2403.13049v1.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":"higher-operations-in-perturbation-theory","repo_url":"https://github.com/twistedqfts/omega-integrand","is_official":1,"mentioned_in_paper":1,"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}