A proof of the conformal collider bounds

Abstract

Abstract: In this paper, we prove that the “conformal collider bounds” originally proposed in [1] hold for any unitary parity-preserving conformal field theory (CFT) with a unique stress tensor in dimensions d ≥ 3. In particular this implies that the ratio of central charges for a unitary 4d CFT lies in the interval 3118≥ac≥13. For superconformal theories this is further reduced to 32≥ac≥12. 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.