Towards celestial CFT dual of 4d conformal gravity: I

TL;DR

This paper computes celestial operator product expansions in a conformal supergravity model, revealing how soft graviton theorems and symmetries manifest in the dual celestial conformal field theory, with implications for celestial holography.

Contribution

It provides the first detailed analysis of celestial OPEs in conformal supergravity, highlighting modifications in soft graviton theorems and the structure of celestial symmetries.

Findings

Soft graviton OPEs match two-derivative gravity in leading order.

Subleading soft graviton OPEs receive non-universal corrections.

Celestial CFT maintains at least chiral BMS4 symmetry, possibly extended.

Abstract

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 $\mathfrak{sl}(2,\mathbb{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 $\mathfrak{bms}_4$ symmetry, though in a non-trivial way, and possibly a conformal extension of it.