Leading Multi-Stress Tensors and Conformal Bootstrap

TL;DR

This paper develops a recursive bootstrap method to compute contributions of multi-stress tensor operators to correlators in conformal field theories across dimensions, confirming the exponentiation of near lightcone correlators.

Contribution

It introduces a novel recursive bootstrap approach to determine multi-stress tensor contributions in any even-dimensional CFT with large central charge.

Findings

Derived OPE coefficients for double- and triple-stress tensors in 4D.

Computed double-stress tensor contributions in 6D.

Confirmed consistency with exponentiation of the near lightcone correlator.

Abstract

Near lightcone correlators are dominated by operators with the lowest twist. We consider the contributions of such leading lowest twist multi-stress tensor operators to a heavy-heavy-light-light correlator in a CFT of any even dimensionality with a large central charge. An infinite number of such operators contribute, but their sum is described by a simple ansatz. We show that the coefficients in this ansatz can be determined recursively, thereby providing an operational procedure to compute them. This is achieved by bootstrapping the corresponding near lightcone correlator: conformal data for any minimal-twist determines that for the higher minimal-twist and so on. To illustrate this procedure in four spacetime dimensions we determine the contributions of double- and triple-stress tensors. We compute the OPE coefficients; whenever results are available in the literature, we observe complete agreement. We also compute the contributions of double-stress tensors in six spacetime dimensions and determine the corresponding OPE coefficients. In all cases the results are consistent with the exponentiation of the near lightcone correlator. This is similar to the situation in two spacetime dimensions for the Virasoro vacuum block.