Universal relation between $C_{T}$ and the CFT Weyl anomaly

Fuente: arXiv
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Main Authors: Aros, Rodrigo, Bugini, Fabrizzio, Diaz, Danilo E., Núñez-Barra, Camilo
Format: Preprint
Published: 2026
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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
id 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