Yang-Mills theory from the worldline
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914876844146688 |
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| author | Bonezzi, Roberto |
| author_facet | Bonezzi, Roberto |
| contents | We construct off-shell vertex operators for the bosonic spinning particle. Using the language of homotopy algebras, we show that the full nonlinear structure of Yang-Mills theory, including its gauge transformations, is encoded in the commutator algebra of the worldline vertex operators. To do so, we deform the worldline BRST operator by coupling it to a background gauge field and show that the coupling is consistent on a suitable truncation of the Hilbert space. On this subspace, the square of the BRST operator is proportional to the Yang-Mills field equations, which we interpret as an operator Maurer-Cartan equation for the background. This allows us to define further vertex operators in different ghost numbers, which correspond to the entire $L_\infty$ algebra of Yang-Mills theory. Besides providing a precise map of a fully nonlinear field theory into a worldline model, we expect these results will be valuable to investigate the kinematic algebra of Yang-Mills, which is central to the double copy program. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19045 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Yang-Mills theory from the worldline Bonezzi, Roberto High Energy Physics - Theory We construct off-shell vertex operators for the bosonic spinning particle. Using the language of homotopy algebras, we show that the full nonlinear structure of Yang-Mills theory, including its gauge transformations, is encoded in the commutator algebra of the worldline vertex operators. To do so, we deform the worldline BRST operator by coupling it to a background gauge field and show that the coupling is consistent on a suitable truncation of the Hilbert space. On this subspace, the square of the BRST operator is proportional to the Yang-Mills field equations, which we interpret as an operator Maurer-Cartan equation for the background. This allows us to define further vertex operators in different ghost numbers, which correspond to the entire $L_\infty$ algebra of Yang-Mills theory. Besides providing a precise map of a fully nonlinear field theory into a worldline model, we expect these results will be valuable to investigate the kinematic algebra of Yang-Mills, which is central to the double copy program. |
| title | Yang-Mills theory from the worldline |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2406.19045 |