Dean Carmi, Joao Penedones, Joao A. Silva, Alexander Zhiboedov
SciPost Phys. 10, 145 (2021) ·
published 14 June 2021
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We use Mellin space dispersion relations together with Polyakov conditions to
derive a family of sum rules for Conformal Field Theories (CFTs). The defining
property of these sum rules is suppression of the contribution of the double
twist operators. Firstly, we apply these sum rules to the Wilson-Fisher model
in $d=4-\epsilon$ dimensions. We re-derive many of the known results to order
$\epsilon^4$ and we make new predictions. No assumption of analyticity down to
spin $0$ was made. Secondly, we study holographic CFTs. We use dispersive sum
rules to obtain tree-level and one-loop anomalous dimensions. Finally, we
briefly discuss the contribution of heavy operators to the sum rules in UV
complete holographic theories.
