Subsubleading soft graviton symmetry and MHV graviton scattering amplitudes

TL;DR

The paper analyzes the role of the subsubleading soft graviton symmetry in the celestial CFT description of tree-level MHV graviton amplitudes. Building on established results that leading and subleading soft theorems (supertranslations and SLbar(2,C) current algebra) fix MHV amplitudes, it introduces subsubleading currents and derives linear relations among their descendants by enforcing consistency with the subsubleading soft theorem and the OPE. It shows that new subsubleading-descendant null states arise but do not provide additional independent constraints, and that the OPE remains invariant under the subsubleading symmetry up to null states. The authors provide both an OPE-based and an algebraic (null-state) derivation of the relations and demonstrate invariance of the subleading OPE terms, reinforcing that, in the MHV sector, the existing asymptotic symmetries suffice to determine full tree-level amplitudes.

Abstract

In arXiv:2008.04330 it was shown that supertranslation and $\overline{SL(2,\mathbb C)}$ current algebra symmetries, corresponding to leading and subleading soft graviton theorems, are enough to determine the tree level MHV graviton scattering amplitudes. In this note we clarify the role of subsubleading soft graviton theorem in this context.