A Shorter Path to Celestial Currents

TL;DR

This paper explores how celestial symmetries and Ward identities can be derived from bulk spacetime considerations, providing a more direct geometric understanding of celestial holography.

Contribution

It introduces a geometric lifting procedure that connects celestial currents to bulk gauge theory boundary integrals, clarifying the origin of celestial Ward identities.

Findings

Celestial symmetries correspond to boundary integrals of bulk gauge fields.

Ward identities follow directly from Noether's theorem applied to these symmetries.

The approach simplifies the derivation of celestial holography results.

Abstract

Here we consider what happens when we lift a codimension-1 slice of the celestial sphere to a codimension-1 slice of the bulk spacetime in a manner that respects our ability to quotient by the null generators of $\mathcal{I}^\pm$ to get to our codimension-2 hologram. The contour integrals of the 2D currents for the celestial symmetries lift to the standard boundary integrals of the 2-form generators for the gauge theory and celestial Ward identities follow directly from Noether's theorem.