MHV Graviton Scattering Amplitudes and Current Algebra on the Celestial Sphere

Understand

The Cachazo-Strominger subleading soft graviton theorem for a positive helicity soft graviton is equivalent to the Ward identities for $\overline{SL(2,\mathbb C)}$ currents.

• This naturally gives rise to a $\overline{SL(2,\mathbb C)}$ current algebra living on the celestial sphere.
• The generators of the $\overline{SL(2,\mathbb C)}$ current algebra and the supertranslations, coming from a positive helicity leading soft graviton, form a closed algebra.
• We find that the OPE of two graviton primaries in the Celestial CFT, extracted from MHV amplitudes, is completely determined in terms of this algebra.