Conformal Collider Physics from the Lightcone Bootstrap

TL;DR

This work analyzes spinning conformal blocks in the 3d lightcone bootstrap, showing that large-spin double-twist operators must exist and that their anomalous dimensions are governed by the exchange of the stress tensor and conserved currents. A central result is that the sign of these anomalous dimensions is negative precisely when conformal collider bounds on three-point functions are satisfied, linking CFT energy flux positivity to attractive bulk gravity in AdS. The authors extend the framework to SU(N) adjoint representations, mixed current-scalar correlators, and TTφφ processes, deriving explicit large-ℓ OPE coefficients and anomalous-dimension formulas that encode gauge binding and gravitational binding energies. They also discuss implications for bulk causality, higher spin symmetry at large N, and superconformal theories, and propose future directions including extensions to higher dimensions and parity-violating cases. Overall, the paper establishes a deep, calculable connection between CFT consistency conditions, collider bounds, and holographic gravity, enriching our understanding of how spin and symmetry data constrain the space of consistent quantum field theories.

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.