Relating diagrammatic expansion with conformal correlator expansion

Sunny Guha; Kallol Sen

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arXiv · 1911.11188

Relating diagrammatic expansion with conformal correlator expansion

Sunny Guha·Kallol Sen

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Abstract

In this note we study the possible connection between functions appearing in diagrammatic expansion and the conformal correlator expansion. To study the connection we propose a generating function which can be expanded to construct a basis. This basis can be utilized to expand, I) the four point function of scalars near the Wilson-Fisher fixed point in $d=4-ε$ as in \cite{Alday:2017zzv} and II) integrals for loop diagrams for massless $ϕ^4$ theory in position space in four dimensions. This suggests that a linear combination of one expansion can be recast in terms of a linear combination of the other. As a by-product, we also derive the Mellin space representation for the twist-2 higher spin conformal blocks. We also discuss the higher derivative contact terms in the present scenario.

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Sunny Guha, Kallol Sen. 2019-11-25. Relating diagrammatic expansion with conformal correlator expansion. https://arxiv.org/abs/1911.11188

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