Higher Operations in Perturbation Theory

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 re...

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Bibliographic Details
Main Authors Gaiotto, Davide, Kulp, Justin, Wu, Jingxiang
Format Journal Article
LanguageEnglish
Published 19.03.2024
Subjects
Mathematics - Quantum Algebra
Physics - High Energy Physics - Theory
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DOI10.48550/arxiv.2403.13049

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Summary: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.
DOI:10.48550/arxiv.2403.13049