Tree-level Scattering Amplitudes via Homotopy Transfer
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866929205570174976 |
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| author | Bonezzi, Roberto Chiaffrino, Christoph Diaz-Jaramillo, Felipe Hohm, Olaf |
| author_facet | Bonezzi, Roberto Chiaffrino, Christoph Diaz-Jaramillo, Felipe Hohm, Olaf |
| contents | We formalize the computation of tree-level scattering amplitudes in terms of the homotopy transfer of homotopy algebras, illustrating it with scalar $ϕ^3$ and Yang-Mills theory. The data of a (gauge) field theory with an action is encoded in a cyclic homotopy Lie or $L_{\infty}$ algebra defined on a chain complex including a space of fields. This $L_{\infty}$ structure can be transported, by means of homotopy transfer, to a smaller space that, in the massless case, consists of harmonic fields. The required homotopy maps are well-defined since we work with the space of finite sums of plane-wave solutions. The resulting $L_{\infty}$ brackets encode the tree-level scattering amplitudes and satisfy generalized Jacobi identities that imply the Ward identities. We further present a method to compute color-ordered scattering amplitudes for Yang-Mills theory, using that its $L_{\infty}$ algebra is the tensor product of the color Lie algebra with a homotopy commutative associative or $C_{\infty}$ algebra. The color-ordered scattering amplitudes are then obtained by homotopy transfer of $C_{\infty}$ algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_09306 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Tree-level Scattering Amplitudes via Homotopy Transfer Bonezzi, Roberto Chiaffrino, Christoph Diaz-Jaramillo, Felipe Hohm, Olaf High Energy Physics - Theory Mathematical Physics We formalize the computation of tree-level scattering amplitudes in terms of the homotopy transfer of homotopy algebras, illustrating it with scalar $ϕ^3$ and Yang-Mills theory. The data of a (gauge) field theory with an action is encoded in a cyclic homotopy Lie or $L_{\infty}$ algebra defined on a chain complex including a space of fields. This $L_{\infty}$ structure can be transported, by means of homotopy transfer, to a smaller space that, in the massless case, consists of harmonic fields. The required homotopy maps are well-defined since we work with the space of finite sums of plane-wave solutions. The resulting $L_{\infty}$ brackets encode the tree-level scattering amplitudes and satisfy generalized Jacobi identities that imply the Ward identities. We further present a method to compute color-ordered scattering amplitudes for Yang-Mills theory, using that its $L_{\infty}$ algebra is the tensor product of the color Lie algebra with a homotopy commutative associative or $C_{\infty}$ algebra. The color-ordered scattering amplitudes are then obtained by homotopy transfer of $C_{\infty}$ algebras. |
| title | Tree-level Scattering Amplitudes via Homotopy Transfer |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2312.09306 |