Logarithmic Celestial Conformal Field Theory

TL;DR

This paper proposes that celestial conformal field theory has a logarithmic structure, featuring Jordan blocks and logarithmic correlators, which helps explain its properties and the role of the stress tensor and Liouville field.

Contribution

It identifies a logarithmic conformal field theory structure within celestial CFT, including Jordan blocks and correlator behaviors, advancing understanding of its mathematical framework.

Findings

Identification of Jordan block structure involving stress tensor

Calculation of two-point correlators showing logarithmic behavior

Discussion of vanishing central charge and its implications

Abstract

We argue that the celestial conformal field theory exhibits patterns of a logarithmic conformal field theory. We uncover a Jordan block structure involving the celestial stress tensor and its logarithmic partner, a composite operator built from the stress tensor and the Liouville field. Using a limiting process whose parameter corresponds to the infrared cut-off of gravity, we perform some basic consistency checks, particularly the calculation of two-point correlators, which reveals the expected logarithmic behavior. We comment on the vanishing value of the central charge in the celestial conformal field theory and explain how the logarithmic partner is relevant for its well-behavedness.