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• W3068113170 abstract "We find the general solution of the conformal Ward identities for scalar $n$-point functions in momentum space and in general dimension. The solution is given in terms of integrals over $(n-1)$-simplices in momentum space. The $n$ operators are inserted at the $n$ vertices of the simplex, and the momenta running between any two vertices of the simplex are the integration variables. The integrand involves an arbitrary function of momentum-space cross ratios constructed from the integration variables, while the external momenta enter only via momentum conservation at each vertex. Correlators where the function of cross ratios is a monomial exhibit a remarkable recursive structure where $n$-point functions are built in terms of $(n-1)$-point functions. To illustrate our discussion, we derive the simplex representation of $n$-point contact Witten diagrams in a holographic conformal field theory. This can be achieved through both a recursive method, as well as an approach based on the star-mesh transformation of electrical circuit theory. The resulting expression for the function of cross ratios involves $(n-2)$ integrations, which is an improvement (when $n>4$) relative to the Mellin representation that involves $n(n-3)/2$ integrations." @default.
• W3068113170 created "2020-08-24" @default.
• W3068113170 creator A5019593911 @default.
• W3068113170 creator A5062550951 @default.
• W3068113170 creator A5074254752 @default.
• W3068113170 date "2021-01-28" @default.
• W3068113170 modified "2023-10-18" @default.
• W3068113170 title "Conformal correlators as simplex integrals in momentum space" @default.
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• W3068113170 doi "https://doi.org/10.1007/jhep01(2021)192" @default.
• W3068113170 hasPublicationYear "2021" @default.
• W3068113170 type Work @default.

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