Recursion relations for 5-point conformal blocks

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...

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Bibliographic Details
Published in:arXiv.org 2022-05
Main Authors: Poland, David, Prilepina, Valentina
Format: Article
Language:English
Subjects:
Operators (mathematics)
Scalars
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2103.12092