On the associativity of 1-loop corrections to the celestial operator product in gravity

TL;DR

This paper investigates the 1-loop corrections to the celestial operator product in gravity, revealing that anomalies prevent associativity in the chiral algebra unless canceled by a gravitational axion or in specific matter-coupled theories.

Contribution

It demonstrates the non-associativity of 1-loop corrected celestial chiral algebras in gravity and proposes mechanisms for anomaly cancellation.

Findings

1-loop corrections induce anomalies in the celestial chiral algebra

Coupling to a 4th-order gravitational axion cancels the anomaly

Certain matter-coupled self-dual gravity theories avoid the anomaly

Abstract

The question of whether the holomorphic collinear singularities of graviton amplitudes define a consistent chiral algebra has garnered much recent attention. We analyse a version of this question for infinitesimal perturbations around the self-dual sector of 4d Einstein gravity. The singularities of tree amplitudes in such perturbations do form a consistent chiral algebra, however at 1-loop its operator products are corrected by the effective graviton vertex. We argue that this chiral algebra can be interpreted as the universal holomorphic surface defect in the twistor uplift of self-dual gravity, and show that the same correction is induced by an anomalous diagram in the bulk-defect system. The 1-loop holomorphic collinear singularities do not form a consistent chiral algebra. The failure of associativity can be traced to the existence of a recently discovered gravitational anomaly on twistor space. It can be restored by coupling to an unusual 4th-order gravitational axion, which cancels the anomaly by a Green-Schwarz mechanism. Alternatively, the anomaly vanishes in certain theories of self-dual gravity coupled to matter, including in self-dual supergravity.