Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Rodrigo Aros, Fabrizzio Bugini, Danilo E. Diaz, Camilo Núñez-Barra

Abstract

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.

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

Abstract

We establish a universal relation between the coefficient of the energy momentum tensor two point function and the coefficient 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 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 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 . Several known examples are revisited to illustrate and validate the general result.
Paper Structure (16 sections, 53 equations)

This paper contains 16 sections, 53 equations.

Table of Contents

  1. Introduction
  2. Universal relation between $C_T$ and $c$ from holographic data
  3. Holographic derivation of $C_T$ from bulk Einstein gravity
  4. Holographic Weyl anomaly for bulk Einstein gravity and $Q$-curvature
  5. Weyl-squared content of the $Q$-curvature
  6. $C_T$ vs. $c$ from holographic data
  7. Universal relation between $C_T$ and $c$ : CFT derivation
  8. Standard derivation in 4D
  9. Alternative derivation in 4D
  10. Standard derivation in 6D
  11. Alternative derivation in 6D
  12. General even dimensions: the standard construction
  13. General even $D$: $Q$-curvature and GJMS-like operators
  14. Examples
  15. Conclusion
  16. ...and 1 more sections