Conformal Collider Physics from the Lightcone Bootstrap

TL;DR

This paper analytically explores the lightcone bootstrap in 3d CFTs, revealing how stress tensor contributions relate to collider bounds and connecting AdS gravity attractiveness with CFT energy positivity.

Contribution

It provides a detailed analysis of the lightcone limit for 4-point functions with currents and stress tensor, establishing new bounds linking CFT data and AdS gravity properties.

Findings

Stress tensor contributions are negative if collider bounds are satisfied.

The sign of gauge binding energy depends on current 3-point function coefficients.

Relations between CFT charge flux bounds and AdS gravity attractiveness are established.

Abstract

We analytically study the lightcone limit of the conformal bootstrap equations for 4-point functions containing global symmetry currents and the stress tensor in 3d CFTs. We show that the contribution of the stress tensor to the anomalous dimensions of large spin double-twist states is negative if and only if the conformal collider physics bounds are satisfied. In the context of AdS/CFT these results indicate a relation between the attractiveness of AdS gravity and positivity of the CFT energy flux. We also study the contribution of non-Abelian conserved currents to the anomalous dimensions of double-twist operators, corresponding to the gauge binding energy of 2-particle states in AdS. We show that the representation of the double-twist state determines the sign of the gauge binding energy if and only if the coefficient appearing in the current 3-point function satisfies a similar bound, which is equivalent to an upper bound on the charge flux asymmetry of the CFT.