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arXiv · 2103.12092

Recursion relations for 5-point conformal blocks

David Poland·Valentina Prilepina
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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.

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David Poland, Valentina Prilepina. 2022-05-19. Recursion relations for 5-point conformal blocks. https://doi.org/10.1007/jhep10(2021)160

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