A Conformal Collider for Holographic CFTs

TL;DR

The paper develops a conformal collider framework for holographic CFTs by introducing a holographic null energy condition, enabling causality-derived bounds directly from three-point functions rather than four-point Regge amplitudes.By analyzing smeared, low-spin operator insertions, the authors derive universal Regge OPE structure expressed as a shockwave in the bulk and connect this to a gravity-like universal behavior for holographic CFTs with large central charge and a gap.The results yield quantitative bounds on a wide set of three-point functions (e.g., $\langle JJT\rangle$, $\langle TTT\rangle$, $\langle O_{\ell=1}O_{\ell=1}T\rangle$, $\langle O_{\ell=2}O_{\ell=2}T\rangle$) and show how these constrain higher-derivative bulk couplings, with distinctive features in $d=3$ (parity structures) and implications for inflationary observables such as chiral gravity waves and tensor mode non-Gaussianity.Overall, the work argues that holographic CFTs with large $c_T$ and sparse spectra admit universal gravity-like dual descriptions, and provides a powerful, three-point–data–driven set of constraints with potential cosmological implications.

Abstract

We develop a formalism to study the implications of causality on OPE coefficients in conformal field theories with large central charge and a sparse spectrum of higher spin operators. The formalism has the interpretation of a new conformal collider-type experiment for these class of CFTs and hence it has the advantage of requiring knowledge only about CFT three-point functions. This is accomplished by considering the holographic null energy operator which was introduced in arXiv:1709.03597 as a generalization of the averaged null energy operator. Analyticity properties of correlators in the Regge limit imply that the holographic null energy operator is a positive operator in a subspace of the total CFT Hilbert space. Utilizing this positivity condition, we derive bounds on three-point functions $\langle TO_1O_2\rangle$ of the stress tensor with various operators for CFTs with large central charge and a sparse spectrum. After imposing these constraints, we also find that the operator product expansions of all primary operators in the Regge limit have certain universal properties. All of these results are consistent with the expectation that CFTs in this class, irrespective of their microscopic details, admit universal gravity-like holographic dual descriptions. Furthermore, this connection enables us to constrain various inflationary observables such as the amplitude of chiral gravity waves, non-gaussanity of gravity waves and tensor-to-scalar ratio.

Figures (4)

• Figure 1: Conformal collider experiment: A localized excitation is created in a holographic CFT and an instrument which is shown in blue, measures the holographic null energy ${\mathcal{E}}_r$ far away from the excitation.
• Figure 2: In the Regge limit the leading correction to the $\psi\psi$ OPE is the graviton $h_{uu}$ integrated over the red line.
• Figure 3: Kinematics for the derivation of the holographic null energy condition. Operators $O$s are smeared over some regions in a Rindler reflection symmetric way.
• Figure 4: The Witten diagram for the correlator $\langle \overline{\varepsilon.O(B)} \, \int du' h_{uu}(u',z=B \sqrt{\rho}) \, \varepsilon.O(B) \rangle$.