Celestial OPE in self-dual gravity

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 aw1+co-invariant theory whose scattering amplitudes are one -loop exact with all positive helicity gravitons. Celestial w1+co symmetry is generated by an infinite tower of (conformally soft) gravitons which are holomorphic conserved currents. We find that at any given order only the descendants of a finite number of w1+co currents contribute to the operator product expansion. This is somewhat surprising but, this is consistent with our earlier analysis based on w1+co symmetry alone. The phenomenon of truncation also suggests that in some (unknown) formulation the spectrum of conformal dimensions in the dual two dimensional theory can be bounded from below.