Celestial two-point functions and rectified dictionary

TL;DR

This paper refines the celestial dictionary to produce standard power-law two-point functions in CCFT, enabling smooth massless limits and providing new three-point function calculations and OPE insights.

Contribution

It introduces a rectified celestial dictionary using shadow transformations, improving the behavior of correlators and facilitating analysis of massless limits in CCFT.

Findings

Two-point functions follow standard power-law behavior

Smooth massless limit achieved with the new dictionary

Computed a three-point function and discussed OPE in CCFT

Abstract

A naive celestial dictionary causes massless two-point functions to take the delta-function forms in the celestial conformal field theory (CCFT). We rectify the dictionary, involving the shadow transformation so that the two-point functions follow the standard power-law. In this new definition, we can smoothly take the massless limit of the massive dictionary. We also compute a three-point function using the new dictionary and discuss the OPE in CCFT.