Higher operations in perturbation theory
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 regul...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-05-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP05(2025)230 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849725458328846336 |
|---|---|
| author | Davide Gaiotto Justin Kulp Jingxiang Wu |
| author_facet | Davide Gaiotto Justin Kulp Jingxiang Wu |
| author_sort | Davide Gaiotto |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-19239a8d6dda4ba2bcb65d5eb3c89a9d |
| institution | DOAJ |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-19239a8d6dda4ba2bcb65d5eb3c89a9d2025-08-20T03:10:28ZengSpringerOpenJournal of High Energy Physics1029-84792025-05-012025517610.1007/JHEP05(2025)230Higher operations in perturbation theoryDavide Gaiotto0Justin Kulp1Jingxiang Wu2Perimeter Institute for Theoretical PhysicsSimons Center for Geometry and Physics, Stony Brook UniversityMathematical Institute, University of OxfordAbstract 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.https://doi.org/10.1007/JHEP05(2025)230BRST QuantizationSupersymmetric Gauge TheoryAnomalies in Field and String TheoriesTopological Field Theories |
| spellingShingle | Davide Gaiotto Justin Kulp Jingxiang Wu Higher operations in perturbation theory Journal of High Energy Physics BRST Quantization Supersymmetric Gauge Theory Anomalies in Field and String Theories Topological Field Theories |
| title | Higher operations in perturbation theory |
| title_full | Higher operations in perturbation theory |
| title_fullStr | Higher operations in perturbation theory |
| title_full_unstemmed | Higher operations in perturbation theory |
| title_short | Higher operations in perturbation theory |
| title_sort | higher operations in perturbation theory |
| topic | BRST Quantization Supersymmetric Gauge Theory Anomalies in Field and String Theories Topological Field Theories |
| url | https://doi.org/10.1007/JHEP05(2025)230 |
| work_keys_str_mv | AT davidegaiotto higheroperationsinperturbationtheory AT justinkulp higheroperationsinperturbationtheory AT jingxiangwu higheroperationsinperturbationtheory |