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- Title
Mellin amplitudes for 1d CFT.
- Authors
Bianchi, Lorenzo; Bliard, Gabriel; Forini, Valentina; Peveri, Giulia
- Abstract
We define a Mellin amplitude for CFT1 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 AdS2 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.
- Subjects
MELLIN transform; COMPLEX variables; CONFORMAL field theory; CORRELATORS; MEROMORPHIC functions
- Publication
Journal of High Energy Physics, 2021, Vol 2021, Issue 10, p1
- ISSN
1126-6708
- Publication type
Article
- DOI
10.1007/JHEP10(2021)095