Universal relation between $C_{T}$ and the CFT Weyl anomaly
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917539596992512 |
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| author | Aros, Rodrigo Bugini, Fabrizzio Diaz, Danilo E. Núñez-Barra, Camilo |
| author_facet | Aros, Rodrigo Bugini, Fabrizzio Diaz, Danilo E. Núñez-Barra, Camilo |
| contents | We establish a universal relation between the coefficient $C_T$ of the energy momentum tensor two point function and the coefficient $c$ multiplying the term quadratic in the Weyl tensor in the Weyl anomaly of a generic even dimensional conformal field theory. Our first derivation combines long known holographic results for $C_T$ and for the Weyl anomaly in Einstein bulk gravity with a recently obtained Chern Gauss Bonnet formula for compact Einstein manifolds. This theorem isolates the Weyl squared contribution in the relation between the Euler density and the $Q$ curvature, allowing us to identify the relevant quadratic term unambiguously. We then provide a genuine CFT derivation based on the renormalization group running of the TT correlator with respect to the arbitrary but necessary mass scale $μ$. Several known examples are revisited to illustrate and validate the general result. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_00321 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Universal relation between $C_{T}$ and the CFT Weyl anomaly Aros, Rodrigo Bugini, Fabrizzio Diaz, Danilo E. Núñez-Barra, Camilo High Energy Physics - Theory General Relativity and Quantum Cosmology We establish a universal relation between the coefficient $C_T$ of the energy momentum tensor two point function and the coefficient $c$ multiplying the term quadratic in the Weyl tensor in the Weyl anomaly of a generic even dimensional conformal field theory. Our first derivation combines long known holographic results for $C_T$ and for the Weyl anomaly in Einstein bulk gravity with a recently obtained Chern Gauss Bonnet formula for compact Einstein manifolds. This theorem isolates the Weyl squared contribution in the relation between the Euler density and the $Q$ curvature, allowing us to identify the relevant quadratic term unambiguously. We then provide a genuine CFT derivation based on the renormalization group running of the TT correlator with respect to the arbitrary but necessary mass scale $μ$. Several known examples are revisited to illustrate and validate the general result. |
| title | Universal relation between $C_{T}$ and the CFT Weyl anomaly |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2603.00321 |