City Research Online

Mellin amplitudes for 1d CFT

Bianchi, L., Bliard, G., Forini, V. ORCID: 0000-0001-9726-1423 & Peveri, G. (2021). Mellin amplitudes for 1d CFT. Journal of High Energy Physics, 2021(10), article number 95. doi: 10.1007/jhep10(2021)095


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.

Publication Type: Article
Additional Information: This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Publisher Keywords: AdS-CFT Correspondence, Conformal Field Theory
Subjects: Q Science > QC Physics
Departments: School of Science & Technology > Mathematics
SWORD Depositor:
[thumbnail of Bianchi2021_Article_MellinAmplituDesFor1DCFT.pdf]
Text - Published Version
Available under License Creative Commons: Attribution International Public License 4.0.

Download (837kB) | Preview


Add to AnyAdd to TwitterAdd to FacebookAdd to LinkedinAdd to PinterestAdd to Email


Downloads per month over past year

View more statistics

Actions (login required)

Admin Login Admin Login