Loop-Corrected Virasoro Symmetry of 4D Quantum Gravity

TL;DR

The paper investigates whether Virasoro (superrotation) symmetry survives in 4D quantum gravity on asymptotically flat spacetimes at one loop. By using a 2D boundary energy-momentum tensor Tzz constructed from soft gravitons, it shows that the universal IR divergence of the one-loop subleading soft graviton theorem generates a divergent correction to the Tzz Ward identity, which can be absorbed by a one-loop renormalization ΔTzz of Tzz. The authors demonstrate that the renormalized tilde{Tzz} preserves the tree-level Virasoro Ward identity (assuming zero finite corrections to the subleading soft factor), providing evidence for a loop-corrected yet intact Virasoro symmetry in the quantum theory. They also discuss limitations and open questions regarding possible finite corrections and the full nonperturbative realization of the symmetry in celestial holography.

Abstract

Recently a boundary energy-momentum tensor $T_{zz}$ has been constructed from the soft graviton operator for any 4D quantum theory of gravity in asymptotically flat space. Up to an "anomaly" which is one-loop exact, $T_{zz}$ generates a Virasoro action on the 2D celestial sphere at null infinity. Here we show by explicit construction that the effects of the IR divergent part of the anomaly can be eliminated by a one-loop renormalization that shifts $T_{zz}$.