A Proof of the Conformal Collider Bounds
  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. 
Diego M. Hofman, Daliang Li, David Meltzer, David Poland, Fernando   Rejon-Barrera
hep-th cond-mat.stat-mech cond-mat.str-el hep-ph