Mellin amplitudes for 1$d$ CFT
Abstract
We define a Mellin amplitude for CFT four-point functions. Its analytical properties are inferred from physical requirements on the correlator. We discuss the analytic continuation that is necessary for a fully nonperturbative definition of the Mellin transform. The resulting bounded, meromorphic function of a single complex variable is used to derive an infinite set of nonperturbative sum rules for CFT data of exchanged operators, which we test on known examples. We then consider the perturbative setup produced by quartic interactions with an arbitrary number of derivatives in a bulk AdS field theory. With our formalism, we obtain a closed-form expression for the Mellin transform of tree-level contact interactions and for the first correction to the scaling dimension of "two-particle" operators exchanged in the generalized free field theory correlator.
Cite
@article{arxiv.2106.00689,
title = {Mellin amplitudes for 1$d$ CFT},
author = {Lorenzo Bianchi and Gabriel Bliard and Valentina Forini and Giulia Peveri},
journal= {arXiv preprint arXiv:2106.00689},
year = {2021}
}
Comments
48 pages, 2 figures, 1 Mathematica notebook attached; v2: enlarged text in Sections 1,3,5, matches published version in JHEP