Celestial OPE in Self Dual Gravity

TL;DR

This paper computes the celestial operator product expansion for positive helicity gravitons in self dual gravity, revealing a finite contribution from $w_{1+ fty}$ descendants and suggesting a bounded spectrum in celestial CFT.

Contribution

It provides the first explicit calculation of the celestial OPE in self dual gravity and uncovers a truncation phenomenon in the $w_{1+ abla}$ symmetry spectrum.

Findings

Finite number of $w_{1+ abla}$ descendants contribute at each order.

The spectrum of conformal dimensions may be bounded from below.

Supports the idea of a bounded spectrum in celestial CFT.

Abstract

In this paper we compute the celestial operator product expansion between two outgoing positive helicity gravitons in the self dual gravity. It has been shown that the self dual gravity is a $ w_{1+\infty} $-invariant theory whose scattering amplitudes are one loop exact with all positive helicity gravitons. Celestial $w_{1+\infty}$ symmetry is generated by an infinite tower of (conformally soft) gravitons which are holomorphic conserved currents. We find that at any given order only a \textit{finite} number of $w_{1+\infty}$ descendants contribute to the OPE. This is somewhat surprising because the spectrum of conformal dimensions in celestial CFT is not bounded from below. However, this is consistent with our earlier analysis based on the representation theory of $w_{1+\infty}$. The phenomenon of truncation suggests that in some (unknown) formulation the spectrum of conformal dimensions in the dual two dimensional theory can be bounded from below.