A proof of the conformal collider bounds

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 $$ frac{31}{18}ge frac{a}{c}ge frac{1}{3} $$ . for superconformal theories this is further reduced to $$ frac{3}{2}ge frac{a}{c}ge frac{1}{2} $$ . 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.