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Recursion Relations in Witten Diagrams and Conformal Partial Waves · Around

2018

Recursion Relations in Witten Diagrams and Conformal Partial Waves

Zhou, Xinan

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We revisit the problem of performing conformal block decomposition of exchange Witten diagrams in the crossed channel.

Using properties of conformal blocks and Witten diagrams, we discover infinitely many linear relations among the crossed channel decomposition coefficients.
These relations allow us to formulate a recursive algorithm that solves the decomposition coefficients in terms of certain seed coefficients.
In one dimensional CFTs, the seed coefficient is the decomposition coefficient of the double-trace operator with the lowest conformal dimension.

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