The Unique Polyakov Blocks

Abstract

In this work we present a closed form expression for Polyakov blocks in Mellin space for arbitrary spin and scaling dimensions. We provide a prescription to fix the contact term ambiguity uniquely by reducing the problem to that of fixing the contact term ambiguity at the level of cyclic exchange amplitudes -- defining cyclic Polyakov blocks -- in terms of which any fully crossing symmetric correlator can be decomposed. We also give another, equivalent, prescription which does not rely on a decomposition into cyclic amplitudes and we underline the relation between cyclic amplitudes and dispersion relations in Mellin space. We extract the OPE data of double-twist operators in the direct channel expansion of the cyclic Polyakov blocks using and extending the analysis of \cite{Sleight:2018epi,Sleight:2018ryu} to include contributions that are non-analytic in spin. The relation between cyclic Polyakov blocks and analytic Bootstrap functionals is underlined.

arXiv comment21 pages + appendices, 1 figure; v2: discussion on the relation with dispersion relations in Mellin space added, version to be published in JHEP

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Cited by in corpus (10)

• From AdS to dS Exchanges: Spectral Representation, Mellin Amplitudes and Crossing
• From dS to AdS and back
• Dispersive CFT Sum Rules
• Gluon Scattering in AdS from CFT
• Crossing Symmetric Dispersion Relations for Mellin Amplitudes
• Conformal correlators as simplex integrals in momentum space
• Dispersion relations and exact bounds on CFT correlators
• Dispersion Formulas in QFTs, CFTs, and Holography
• Bootstrapping Witten diagrams via differential representation in Mellin space
• Superconformal blocks in diverse dimensions and $BC$ symmetric functions