Higher Operations in Perturbation Theory
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916167086505984 |
|---|---|
| author | Gaiotto, Davide Kulp, Justin Wu, Jingxiang |
| author_facet | Gaiotto, Davide Kulp, Justin Wu, Jingxiang |
| contents | 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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13049 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher Operations in Perturbation Theory Gaiotto, Davide Kulp, Justin Wu, Jingxiang High Energy Physics - Theory Quantum Algebra 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. |
| title | Higher Operations in Perturbation Theory |
| topic | High Energy Physics - Theory Quantum Algebra |
| url | https://arxiv.org/abs/2403.13049 |