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Conformal $n$-point functions in momentum space

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arxiv 1910.10162 v3 pith:XO7NFSI5 submitted 2019-10-22 hep-th cond-mat.stat-mechcond-mat.str-elhep-ph

Adam Bzowski , Paul McFadden , Kostas Skenderis This is my paper · ORCID
classification hep-thcond-mat.stat-mechcond-mat.str-elhep-ph
keywords conformalfunctionspointcasefieldfunctionmomentamomentum-space
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We present a Feynman integral representation for the general momentum-space scalar $n$-point function in any conformal field theory. This representation solves the conformal Ward identities and features an arbitrary function of $n(n-3)/2$ variables which play the role of momentum-space conformal cross-ratios. It involves $(n-1)(n-2)/2$ integrations over momenta, with the momenta running over the edges of an $(n-1)$-simplex. We provide the details in the simplest non-trivial case (4-point functions), and for this case we identify values of the operator and spacetime dimensions for which singularities arise leading to anomalies and beta functions, and discuss several illustrative examples from perturbative quantum field theory and holography.

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Cited by 5 Pith papers

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