d > 2 stress-tensor operator product expansion near a line

We study the operator product expansion of stress tensors (TT OPE) in d > 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: [L-m, L-n] = (m - n)Lm+n + C-m (m(2) - 1)delta(m+n, 0). The dimensionless constant C is proportional to the central charge C-T. Transverse integrals in the definition of L-m 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 > 2 near-lightcone stress-tensor conformal block and the d = 2W algebra is observed. This note is motivated by the search for a field-theoretic derivation of d > 2 correlators in strong coupling critical phenomena.

Automated summary

In this study, the operator product expansion of stress tensors in conformal field theories with a bulk dual of Einstein gravity in d > 2 dimensions was investigated. An algebraic structure consistent with the Jacobi identity was obtained from the TT OPE in a certain null-like limit, with a dimensionless constant C proportional to the central charge. Transverse integrals play a crucial role in the definition of L-m, and a connection between near-lightcone stress-tensor conformal block in d > 2 dimensions and the d = 2W algebra was observed.