Vertex operators for the kinematic algebra of Yang-Mills theory
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916375777247232 |
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| author | Bonezzi, Roberto Chiaffrino, Christoph Hohm, Olaf |
| author_facet | Bonezzi, Roberto Chiaffrino, Christoph Hohm, Olaf |
| contents | The kinematic algebra of Yang-Mills theory can be understood in the framework of homotopy algebras: the $L_{\infty}$ algebra of Yang-Mills theory is the tensor product of the color Lie algebra and a kinematic space that carries a $C_{\infty}$ algebra. There are also hidden structures that generalize Batalin-Vilkovisky algebras, which explain color-kinematics duality and the double copy but are only partially understood. We show that there is a representation of the $C_{\infty}$ algebra, in terms of vertex operators, on the Hilbert space of a first-quantized worldline theory. To this end we introduce $A_{\infty}$ morphisms, which define the vertex operators and which inject the $C_{\infty}$ algebra into the strictly associative algebra of operators on the Hilbert space. We also take first steps to represent the hidden structures on the same space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_17341 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Vertex operators for the kinematic algebra of Yang-Mills theory Bonezzi, Roberto Chiaffrino, Christoph Hohm, Olaf High Energy Physics - Theory Mathematical Physics The kinematic algebra of Yang-Mills theory can be understood in the framework of homotopy algebras: the $L_{\infty}$ algebra of Yang-Mills theory is the tensor product of the color Lie algebra and a kinematic space that carries a $C_{\infty}$ algebra. There are also hidden structures that generalize Batalin-Vilkovisky algebras, which explain color-kinematics duality and the double copy but are only partially understood. We show that there is a representation of the $C_{\infty}$ algebra, in terms of vertex operators, on the Hilbert space of a first-quantized worldline theory. To this end we introduce $A_{\infty}$ morphisms, which define the vertex operators and which inject the $C_{\infty}$ algebra into the strictly associative algebra of operators on the Hilbert space. We also take first steps to represent the hidden structures on the same space. |
| title | Vertex operators for the kinematic algebra of Yang-Mills theory |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2408.17341 |