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Anomalous dimensions at finite conformal spin from OPE inversion · Around

2018

Anomalous dimensions at finite conformal spin from OPE inversion

Cardona, Carlos, Sen, Kallol

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We compute anomalous dimensions of higher spin operators in Conformal Field Theory at arbitrary space-time dimension by using the OPE inversion formula of \cite{Caron-Huot:2017vep}, both from the position space representation as well as from the integral (viz.

Mellin) representation of the conformal blocks.
The Mellin space is advantageous over the position space not only in allowing to write expressions agnostic to the space-time dimension, but also in that it replaces tedious recursion relations in terms of simple sums which are easy to perform.
We evaluate the contributions of scalar and spin exchanges in the $t-$channel exactly, in terms of higher order Hypergeometric functions.

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