Asymptotic Symmetries and Celestial CFT

TL;DR

This paper unifies the understanding of conformally soft modes in celestial CFT, clarifies their role in the basis of wavefunctions, and links asymptotic symmetries like superrotations to conformal primary structures.

Contribution

It demonstrates how conformally soft Goldstone modes are incorporated into the principal series basis and connects superrotation symmetries with shadow transforms in celestial CFT.

Findings

Conformally soft modes are part of the principal series basis.

Shadow superrotations generate non-meromorphic diffeomorphisms.

Virasoro and Diff(S^2) symmetries are unified in this framework.

Abstract

We provide a unified treatment of conformally soft Goldstone modes which arise when spin-one or spin-two conformal primary wavefunctions become pure gauge for certain integer values of the conformal dimension $\Delta$. This effort lands us at the crossroads of two ongoing debates about what the appropriate conformal basis for celestial CFT is and what the asymptotic symmetry group of Einstein gravity at null infinity should be. Finite energy wavefunctions are captured by the principal continuous series $\Delta\in 1+i\mathbb{R}$ and form a complete basis. We show that conformal primaries with analytically continued conformal dimension can be understood as certain contour integrals on the principal series. This clarifies how conformally soft Goldstone modes fit in but do not augment this basis. Conformally soft gravitons of dimension two and zero which are related by a shadow transform are shown to generate superrotations and non-meromorphic diffeomorphisms of the celestial sphere which we refer to as shadow superrotations. This dovetails the Virasoro and Diff(S$^2$) asymptotic symmetry proposals and puts on equal footing the discussion of their associated soft charges, which correspond to the stress tensor and its shadow in the two-dimensional celestial CFT.