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 a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>w</a:mi><a:mrow><a:mn>1</a:mn><a:mo>+</a:mo><a:mi>∞</a:mi></a:mrow></a:msub></a:math>-invariant theory whose scattering amplitudes are one-loop exact with all positive helicity gravitons. Celestial <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>w</c:mi><c:mrow><c:mn>1</c:mn><c:mo>+</c:mo><c:mi>∞</c:mi></c:mrow></c:msub></c:math> 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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>w</e:mi><e:mrow><e:mn>1</e:mn><e:mo>+</e:mo><e:mi>∞</e:mi></e:mrow></e:msub></e:math> currents contribute to the operator product expansion. This is somewhat surprising but, this is consistent with our earlier analysis based on <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>w</g:mi><g:mrow><g:mn>1</g:mn><g:mo>+</g:mo><g:mi>∞</g:mi></g:mrow></g:msub></g:math> 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. Published by the American Physical Society 2024