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Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity

Xian O. Camanho, Jose D. Edelstein

TL;DR

This work demonstrates a precise correspondence between causality constraints in Gauss-Bonnet gravity and positivity bounds from conformal collider energy flux in dual CFTs, extending the analysis from 6d theories to arbitrary dimensions. Through black hole perturbations and graviton–shock wave scattering, the authors derive helicity-dependent bounds on the GB coupling λ that precisely match the CFT-derived bounds on t2 and t4, validating the AdS/CFT framework beyond Einstein gravity. They provide explicit dimension-dependent formulas, showing upper bounds that saturate at known values in 5d and 7d and approach a finite limit as dimension grows, with broader implications for η/s and the existence of higher-dimensional CFTs. The results reinforce the deep link between causality and energy positivity in holography and stimulate further exploration of curvature corrections in holographic duals and their field-theoretic interpretations.

Abstract

We explore the relation between positivity of the energy constraints in conformal field theories and causality in their dual gravity description. Our discussion involves CFTs with different central charges whose description, in the gravity side, requires the inclusion of quadratic curvature corrections. It is enough, indeed, to consider the Gauss-Bonnet term. We find that both sides of the AdS/CFT correspondence impose a restriction on the Gauss-Bonnet coupling. In the case of 6d supersymmetric CFTs, we show the full matching of these restrictions. We perform this computation in two ways. First by considering a thermal setup in a black hole background. Second by scrutinizing the scattering of gravitons with a shock wave in AdS. The different helicities provide the corresponding lower and upper bounds. We generalize these results to arbitrary higher dimensions and comment on some hints and puzzles they prompt regarding the possible existence of higher dimensional CFTs and the extent to which the AdS/CFT correspondence would be valid for them.

Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity

TL;DR

This work demonstrates a precise correspondence between causality constraints in Gauss-Bonnet gravity and positivity bounds from conformal collider energy flux in dual CFTs, extending the analysis from 6d theories to arbitrary dimensions. Through black hole perturbations and graviton–shock wave scattering, the authors derive helicity-dependent bounds on the GB coupling λ that precisely match the CFT-derived bounds on t2 and t4, validating the AdS/CFT framework beyond Einstein gravity. They provide explicit dimension-dependent formulas, showing upper bounds that saturate at known values in 5d and 7d and approach a finite limit as dimension grows, with broader implications for η/s and the existence of higher-dimensional CFTs. The results reinforce the deep link between causality and energy positivity in holography and stimulate further exploration of curvature corrections in holographic duals and their field-theoretic interpretations.

Abstract

We explore the relation between positivity of the energy constraints in conformal field theories and causality in their dual gravity description. Our discussion involves CFTs with different central charges whose description, in the gravity side, requires the inclusion of quadratic curvature corrections. It is enough, indeed, to consider the Gauss-Bonnet term. We find that both sides of the AdS/CFT correspondence impose a restriction on the Gauss-Bonnet coupling. In the case of 6d supersymmetric CFTs, we show the full matching of these restrictions. We perform this computation in two ways. First by considering a thermal setup in a black hole background. Second by scrutinizing the scattering of gravitons with a shock wave in AdS. The different helicities provide the corresponding lower and upper bounds. We generalize these results to arbitrary higher dimensions and comment on some hints and puzzles they prompt regarding the possible existence of higher dimensional CFTs and the extent to which the AdS/CFT correspondence would be valid for them.

Paper Structure

This paper contains 15 sections, 102 equations.

Table of Contents

  1. Introduction
  2. Aspects of 6d CFTs and conformal collider physics
  3. Gauss-Bonnet theory
  4. Black hole perturbations
  5. Helicity two perturbation
  6. Helicity one perturbation
  7. Helicity zero perturbation
  8. Gravitons colliding shock waves
  9. Helicity two graviton
  10. Helicity one graviton
  11. Helicity zero graviton
  12. Generalization to higher dimensions
  13. Black hole perturbations
  14. Shock waves
  15. Discussion