Mellin amplitudes for 1d CFT

A bstract We define a Mellin amplitude for CFT 1 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, me...

Full description

Saved in:
Bibliographic Details
Published in:The journal of high energy physics 2021-10, Vol.2021 (10), p.1-49, Article 95
Main Authors: Bianchi, Lorenzo, Bliard, Gabriel, Forini, Valentina, Peveri, Giulia
Format: Article
Language:English
Subjects:
AdS-CFT Correspondence
Amplitudes
Classical and Quantum Gravitation
Complex variables
Conformal Field Theory
Elementary Particles
Field theory
High energy physics
Kinematics
Mathematical analysis
Mellin transforms
Meromorphic functions
Operators (mathematics)
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Sum rules
Symmetry
Variables
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A bstract We define a Mellin amplitude for CFT 1 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 2 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.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP10(2021)095