Recursion relations for 5-point conformal blocks
Abstract
We consider 5-point functions in conformal field theories in d > 2 dimensions. Using weight-shifting operators, we derive recursion relations which allow for the computation of arbitrary conformal blocks appearing in 5-point functions of scalar operators, reducing them to a linear combination of blocks with scalars exchanged. We additionally derive recursion relations for the conformal blocks which appear when one of the external operators in the 5-point function has spin 1 or 2. Our results allow us to formulate positivity constraints using 5-point functions which describe the expectation value of the energy operator in bilocal states created by two scalars.
Cite
@article{arxiv.2103.12092,
title = {Recursion relations for 5-point conformal blocks},
author = {David Poland and Valentina Prilepina},
journal= {arXiv preprint arXiv:2103.12092},
year = {2022}
}
Comments
104 pages, 1 attached Mathematica notebook; V2: small adjustments, references added; V3: clarifications and some formulas corrected