Journal Article

Distributions in CFT. Part I. Cross-ratio space

Qiao, Jiaxin, Kravchuk, Petr, Rychkov, Slava

2020

Overview

A bstract We show that the four-point functions in conformal field theory are defined as distributions on the boundary of the region of convergence of the conformal block expansion. The conformal block expansion converges in the sense of distributions on this boundary, i.e. it can be integrated term by term against appropriate test functions. This can be interpreted as a giving a new class of functionals that satisfy the swapping property when applied to the crossing equation, and we comment on the relation of our construction to other types of functionals. Our language is useful in all considerations involving the boundary of the region of convergence, e.g. for deriving the dispersion relations. We establish our results by elementary methods, relying only on crossing symmetry and the standard convergence properties of the conformal block expansion. This is the first in a series of papers on distributional properties of correlation functions in conformal field theory.

• Publisher: Springer Berlin Heidelberg,Springer Nature B.V,Springer,Springer Berlin,SpringerOpen
• Subject: Classical and Quantum Gravitation / Conformal and W Symmetry / Conformal Field Theory / Convergence / Correlation / Elementary Particles / Field Theories in Higher Dimensions / Field Theories in Lower Dimensions / Field theory / Functionals / High energy physics / High Energy Physics - Theory / Mathematical Physics / Physics / Physics and Astronomy / PHYSICS OF ELEMENTARY PARTICLES AND FIELDS / Quantum Field Theories / Quantum Field Theory / Quantum Physics / Regular Article - Theoretical Physics / Relativity Theory / String Theory