# Primary Fields in Celestial CFT

## TL;DR

This paper explores the structure of celestial conformal field theory (CCFT) by deriving the operator product expansion of the energy-momentum tensor with gauge boson operators, revealing their Virasoro primary nature.

## Contribution

It establishes the transformation properties of CCFT operators under celestial sphere diffeomorphisms, advancing the understanding of CCFT symmetries and operator structure.

## Key findings

- Operators transform as Virasoro primaries.
- Derived the OPE of energy-momentum tensor with gauge operators.
- Confirmed the conformal symmetry structure of CCFT.

## Abstract

The basic ingredient of CCFT holography is to regard four-dimensional amplitudes describing conformal wave packets as two-dimensional conformal correlation functions of the operators associated to external particles. By construction, these operators transform as quasi-primary fields under SL(2,C) conformal symmetry group of the celestial sphere. We derive the OPE of the CCFT energy-momentum tensor with the operators representing gauge bosons and show that they transform as Virasoro primaries under diffeomorphisms of the celestial sphere.