Loop-Corrected Virasoro Symmetry of 4D Quantum Gravity

TL;DR

This paper demonstrates how to eliminate IR divergences in the Virasoro symmetry of 4D quantum gravity by a one-loop renormalization of the boundary energy-momentum tensor, clarifying the quantum structure of celestial symmetries.

Contribution

It provides an explicit construction showing the removal of IR divergences in the Virasoro symmetry through a one-loop shift of the boundary energy-momentum tensor.

Findings

IR divergences can be absorbed by a one-loop renormalization.

The Virasoro symmetry remains well-defined after renormalization.

The anomaly affecting the symmetry is one-loop exact and can be controlled.

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 $T_{zz}$.