Diffeomorphism Symmetry in Two Dimensions and Celestial Holography

TL;DR

This paper clarifies why celestial holography's conformal symmetry should not be extended to full diffeomorphism symmetry, using an operator algebra approach to 2D diffeomorphisms and Virasoro algebra.

Contribution

It provides a detailed algebraic analysis of 2D diffeomorphism symmetry and argues against extending celestial holography symmetry beyond conformal symmetry.

Findings

Diffeomorphism symmetry in 2D can be described by an algebra extension of Virasoro.

The paper explains why celestial holography should not have extended diffeomorphism symmetry.

The algebraic framework may be useful for other theoretical investigations.

Abstract

Two-dimensional diffeomorphism symmetry can be described by an operator algebra extension of the well-known Virasoro algebra description of conformal symmetry. Utilizing this extension, this note explains why the conformal symmetry that appears in celestial holography should not be extended to diffeomorphism symmetry, a possibility that several authors have proposed. The description of the two-dimensional diffeomorphism algebra presented here might be useful for other purposes.