A Proof of the Conformal Collider Bounds

TL;DR

This paper provides a rigorous proof, based on bootstrap methods, that conformal collider bounds hold for any unitary parity-preserving conformal field theory with a unique stress tensor, establishing bounds on central charge ratios.

Contribution

It offers the first complete field theory proof of conformal collider bounds using bootstrap techniques, applicable to higher-dimensional unitary CFTs.

Findings

Proves bounds on the ratio of central charges in 4d CFTs.

Establishes bounds for superconformal theories.

Relates bounds to deep inelastic scattering results.

Abstract

In this paper, we prove that the "conformal collider bounds" originally proposed by Hofman and Maldacena hold for any unitary parity-preserving conformal field theory (CFT) with a unique stress tensor in spacetime dimensions larger than 2. In particular this implies that the ratio of central charges for a unitary 4d CFT lies in the interval $\frac{31}{18} \geq \frac{a}{c} \geq \frac{1}{3}$. For superconformal theories this is further reduced to $\frac{3}{2} \geq \frac{a}{c} \geq \frac{1}{2}$. The proof relies only on CFT first principles - in particular, bootstrap methods - and thus constitutes the first complete field theory proof of these bounds. We further elaborate on similar bounds for non-conserved currents and relate them to results obtained recently from deep inelastic scattering.