(Chiral) Virasoro invariance of the tree-level MHV graviton scattering amplitudes

TL;DR

This work demonstrates that the tree-level MHV graviton OPE in celestial holography is invariant under the full Virasoro algebra, indicating the dual celestial theory is a chiral 2D CFT with an extended symmetry algebra combining Virasoro, anti-holomorphic SL(2,C) current algebra, and supertranslations. The authors explicitly verify L_2 invariance and show the OPE can be organized into Virasoro primaries and descendants, with descendant coefficients fixed by Virasoro symmetry independent of the central charge. They discuss the appearance of a holomorphic stress tensor as the shadow of the subleading conformally soft graviton and point to puzzles regarding the interplay between Virasoro and SL(2,C) symmetries. The results support the celestial CFT conjecture for flat-space holography and lay groundwork for further exploration of higher-order terms and soft symmetry extensions.

Abstract

In this paper we continue our study of the tree level MHV graviton scattering amplitudes from the point of view of celestial holography. In arXiv:2008.04330 we showed that the celestial OPE of two gravitons in the MHV sector can be written as a linear combination of $\overline{SL(2,\mathbb C)}$ current algebra and supertranslation descendants. In this note we show that the OPE is in fact manifestly invariant under the infinite dimensional Virasoro algebra as is expected for a $2$-D CFT. This is consistent with the conjecture that the holographic dual in $4$-D asymptotically flat space time is a $2$-D CFT. Since we get only one copy of the Virasoro algebra we can conclude that the holographic dual theory which computes the MHV amplitudes is a chiral CFT with a host of other infinite dimensional global symmetries including $\overline{SL(2,\mathbb C)}$ current algebra, supertranslations and subsubleading soft graviton symmetry. We also discuss some puzzles related to the appearance of the Virasoro symmetry.