Resummation at finite conformal spin

Abstract

We generalize the computation of anomalous dimension and correction to OPE coefficients at finite conformal spin considered recently in \cite{arXiv:1806.10919, arXiv:1808.00612} to arbitrary space-time dimensions. By using the inversion formula of Caron-Huot and the integral (Mellin) representation of conformal blocks, we show that the contribution from individual exchanges to anomalous dimensions and corrections to the OPE coefficients for "double-twist" operators $[{\mathcal{O}}_1{\mathcal{O}}_2{]}_{\Delta ,J}$ in $s-$channel can be written at finite conformal spin in terms of generalized Wilson polynomials. This approach is democratic {\it wrt} space-time dimensions, thus generalizing the earlier findings to cases where closed form expressions of the conformal blocks are not available.

arXiv commentTypos corrected, references added. JHEP version

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• The Inversion Formula and 6j Symbol for 3d Fermions
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• Four-point correlation modular bootstrap for OPE densities