Spinning Mellin Bootstrap: Conformal Partial Waves, Crossing Kernels and Applications

DOI10.1002/PROP.201800038arXiv1804.09334WikidataQ129455762 ScholiaQ129455762MaRDI QIDQ6084551

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Publication date: 6 November 2023

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Abstract: We study conformal partial waves (CPWs) in Mellin space with totally symmetric external operators of arbitrary integer spin. The exchanged spin is arbitrary, and includes mixed symmetry and (partially)-conserved representations. In a basis of CPWs recently introduced in arXiv:1702.08619, we find a remarkable factorisation of the external spin dependence in their Mellin representation. This property allows a relatively straightforward study of inversion formulae to extract OPE data from the Mellin representation of spinning 4pt correlators and in particular, to extract closed-form expressions for crossing kernels of spinning CPWs in terms of the hypergeometric function ${}_4{F}_3$. We consider numerous examples involving both arbitrary internal and external spins, and for both leading and sub-leading twist operators. As an application, working in general $d$ we extract new results for $calOleft(1/Night)$ anomalous dimensions of double-trace operators induced by double-trace deformations constructed from single-trace operators of generic twist and integer spin. In particular, we extract the anomalous dimensions of double-trace operators $[mathcal{O}_{J}Phi{]}_{n,l}$ with ${calO}_J$ a single-trace operator of integer spin $J$.

Full work available at URL: https://arxiv.org/abs/1804.09334

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