Towards celestial CFT dual of 4d conformal gravity: I

We compute tree-level celestial operator product expansions (OPE) in a bosonic sub-sector of the Berkovits-Witten conformal supergravity from the scattering amplitudes in the MHV configuration. While the OPE between a leading soft graviton current for a positive helicity graviton and any of the primary operators exhibits the same singularity structure as in a gravitational theory with two-derivative kinetic terms, the OPE of a subleading soft graviton current with a positive helicity hard graviton primary operator receives corrections, as a consequence of the non-universal nature of the subleading soft graviton theorem in the bulk. Remarkably, the subleading soft graviton terms remain consistent with the Ward identity of the chiral sl(2,R) current algebra, albeit with a different realisation where particle-changing operators play a role. Our analysis suggests that the dual celestial CFT continues to enjoy at least the chiral bms₄ symmetry, though in a non-trivial way, and possibly a conformal extension of it.