<math><mi>d</mi><mo>></mo><mn>2</mn></math> stress-tensor operator product expansion near a line

We study the operator product expansion of stress tensors (TT OPE) in d&gt;2 conformal field theories whose bulk dual is Einstein gravity. Directly from the TT OPE, we obtain, in a certain null-like limit, an algebraic structure consistent with the Jacobi identity: [Lm,Ln]=(m−n)Lm+n+Cm(m2−1)δm+n,0. The dimensionless constant C is proportional to the central charge CT. Transverse integrals in the definition of Lm play a crucial role. We comment on the corresponding limiting procedure and point out a curiosity related to the central term. A connection between the d&gt;2 near-lightcone stress-tensor conformal block and the d=2 W algebra is observed. This note is motivated by the search for a field-theoretic derivation of d&gt;2 correlators in strong coupling critical phenomena.