(Chiral) Virasoro invariance of the tree-level MHV graviton scattering amplitudes
Shamik Banerjee, Sudip Ghosh, Partha Paul
Abstract
A bstract 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 $$ \overline{\mathrm{SL}\left(2,\mathbb{C}\right)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mrow><mml:mi>SL</mml:mi><mml:mfenced><mml:mn>2</mml:mn><mml:mi>ℂ</mml:mi></mml:mfenced></mml:mrow><mml:mo>¯</mml:mo></mml:mover></mml:math> 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 $$ \overline{\mathrm{SL}\left(2,\mathbb{C}\right)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mrow><mml:mi>SL</mml:mi><mml:mfenced><mml:mn>2</mml:mn><mml:mi>ℂ</mml:mi></mml:mfenced></mml:mrow><mml:mo>¯</mml:mo></mml:mover></mml:math> current algebra, supertranslations and subsubleading soft graviton symmetry. We also discuss some puzzles related to the appearance of the Virasoro symmetry.