Resummation at finite conformal spin

Abstract

Abstract We generalize the computation of anomalous dimension and correction to OPE coefficients at finite conformal spin considered recently in [1, 2] 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 O 1 O 2 Δ , J $$ {\left[{\mathcal{O}}_1{\mathcal{O}}_2\right]}_{\Delta, J} $$ in s-channel can be written at finite conformal spin in terms of generalized Wilson polynomials. This approach is democratic with respect to space-time dimensions, thus generalizing the earlier findings to cases where closed form expressions of the conformal blocks are not available.

Keywords

• Conformal Field Theory
• Field Theories in Higher Dimensions