Towards celestial CFT dual of 4d conformal gravity: I

TL;DR

The authors probe the celestial CFT dual of 4d conformal gravity (Berkovits–Witten theory) by computing tree-level celestial OPEs in a bosonic sector using 6- and 5-point MHV amplitudes. They find that while the leading soft-graviton OPE remains universal as in Einstein-type theories, the subleading soft-graviton OPE receives bulk-dependent corrections, interpreted as particle-changing effects that still respect a chiral \\mathfrak{sl}(2,\\mathbb{R}) current algebra but in a nonstandard representation. The results suggest the celestial CFT retains at least chiral \\mathfrak{bms}_4 symmetry and potentially a conformal extension, offering a diagnostic to distinguish Einstein-type bulk gravity from higher-derivative theories via celestial OPEs. The analysis also parallels behaviors seen in (DF)^2 gauge theory, where soft theorems and current algebras persist with modified realizations, reinforcing the role of celestial methods in probing bulk symmetries and holography. Overall, the work advances understanding of how conformal gravity in the bulk manifests in the associated celestial CFT and frames future exploration of hidden symmetry algebras and holographic interpretations.

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.

Figures (2)

• Figure 1: 4-point amplitudes with gluon as an internal propagator
• Figure 2: 4-point amplitudes with scalar as an internal propagator