Double Copy of 3D Chern-Simons Theory and 6D Kodaira-Spencer Gravity
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| author | Bonezzi, Roberto Diaz-Jaramillo, Felipe Hohm, Olaf |
| author_facet | Bonezzi, Roberto Diaz-Jaramillo, Felipe Hohm, Olaf |
| contents | We apply an algebraic double copy construction of gravity from gauge theory to three-dimensional (3D) Chern-Simons theory. The kinematic algebra ${\cal K}$ is the 3D de Rham complex of forms equipped, for a choice of metric, with a graded Lie algebra that is equivalent to the Schouten-Nijenhuis bracket on polyvector fields. The double copied gravity is defined on a subspace of ${\cal K}\otimes \bar{\cal K}$ and yields a topological double field theory for a generalized metric perturbation and two 2-forms. This local and gauge invariant theory is non-Lagrangian but can be rendered Lagrangian by abandoning locality. Upon fixing a gauge this reduces to the double copy of Chern-Simons theory previously proposed by Ben-Shahar and Johansson. Furthermore, using complex coordinates in $\mathbb{C}^3$ this theory is related to six-dimensional (6D) Kodaira-Spencer gravity in that truncating the two 2-forms and one equation yields the Kodaira-Spencer equations on a 3D real slice of $\mathbb{C}^3$. The full 6D Kodaira-Spencer theory can instead be obtained as a consistent truncation of a chiral double copy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16830 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Double Copy of 3D Chern-Simons Theory and 6D Kodaira-Spencer Gravity Bonezzi, Roberto Diaz-Jaramillo, Felipe Hohm, Olaf High Energy Physics - Theory We apply an algebraic double copy construction of gravity from gauge theory to three-dimensional (3D) Chern-Simons theory. The kinematic algebra ${\cal K}$ is the 3D de Rham complex of forms equipped, for a choice of metric, with a graded Lie algebra that is equivalent to the Schouten-Nijenhuis bracket on polyvector fields. The double copied gravity is defined on a subspace of ${\cal K}\otimes \bar{\cal K}$ and yields a topological double field theory for a generalized metric perturbation and two 2-forms. This local and gauge invariant theory is non-Lagrangian but can be rendered Lagrangian by abandoning locality. Upon fixing a gauge this reduces to the double copy of Chern-Simons theory previously proposed by Ben-Shahar and Johansson. Furthermore, using complex coordinates in $\mathbb{C}^3$ this theory is related to six-dimensional (6D) Kodaira-Spencer gravity in that truncating the two 2-forms and one equation yields the Kodaira-Spencer equations on a 3D real slice of $\mathbb{C}^3$. The full 6D Kodaira-Spencer theory can instead be obtained as a consistent truncation of a chiral double copy. |
| title | Double Copy of 3D Chern-Simons Theory and 6D Kodaira-Spencer Gravity |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2404.16830 |