A Compact Formula for Conserved Three-Point Tensor Structures in 4D CFT
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918278139478016 |
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| author | Heslop, Paul Ramisa, Hector Puerta |
| author_facet | Heslop, Paul Ramisa, Hector Puerta |
| contents | We derive a compact analytic formula for a complete basis of conformally invariant tensor structures for three-point functions of conserved operators in arbitrary 4D Lorentz representations. The construction follows directly from a novel constraint equivalent to applying conservation conditions at each point: the leading terms in all OPE limits appear as symmetric traceless tensors. We derive this by lifting to a unified $\mathrm{SU}(m,m|2n)$ analytic superspace framework, where the conservation conditions are automatically solved and then reducing back to 4D CFT. The same method is also used for cases involving one non-conserved operator. This formalism further reveals a map of the counting of CFT tensor structures to that of finite-dimensional $\mathrm{SU}(2n)$ representations, solved by Littlewood-Richardson coefficients. All results can be directly re-interpreted as three-point $\mathcal{N}=2$ and $\mathcal{N}=4$ superconformal tensor structures via the unified analytic superspace. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14618 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Compact Formula for Conserved Three-Point Tensor Structures in 4D CFT Heslop, Paul Ramisa, Hector Puerta High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics We derive a compact analytic formula for a complete basis of conformally invariant tensor structures for three-point functions of conserved operators in arbitrary 4D Lorentz representations. The construction follows directly from a novel constraint equivalent to applying conservation conditions at each point: the leading terms in all OPE limits appear as symmetric traceless tensors. We derive this by lifting to a unified $\mathrm{SU}(m,m|2n)$ analytic superspace framework, where the conservation conditions are automatically solved and then reducing back to 4D CFT. The same method is also used for cases involving one non-conserved operator. This formalism further reveals a map of the counting of CFT tensor structures to that of finite-dimensional $\mathrm{SU}(2n)$ representations, solved by Littlewood-Richardson coefficients. All results can be directly re-interpreted as three-point $\mathcal{N}=2$ and $\mathcal{N}=4$ superconformal tensor structures via the unified analytic superspace. |
| title | A Compact Formula for Conserved Three-Point Tensor Structures in 4D CFT |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2512.14618 |