Lightcone commutator and stress-tensor exchange in d > 2 conformal field theories

Motivated by developing a field-theoretic algebraic approach to the universal part of the stress-tensor sector of a scalar four-point function in a class of higher-dimensional conformal field theories (CFTs), we construct a mode operator, L-m, near the lightcone in d = 4 CFTs and show that it leads to a Virasoro-like commutator, including a regularized central-term. As an example, we describe how to reproduce the d = 4 single-stress tensor exchange contribution in the lightcone limit by a mode summation. A general-d extension is included. We comment on possible generalizations.