Quantizing the non-linear graviton

TL;DR

This paper investigates quantum anomalies in holomorphic Poisson-BF theory on twistor space, revealing conditions under which anomalies cancel and integrability of self-dual gravity is restored, with implications for quantum gravity models.

Contribution

It identifies anomaly cancellation mechanisms in holomorphic Poisson-BF theory coupled with self-dual Yang-Mills, restoring integrability in quantum self-dual gravity.

Findings

All anomalies can be canceled by coupling to a twistor axion field.

When anomalies are canceled, all n≥4-point amplitudes vanish.

Restoration of integrability in quantum self-dual gravity achieved.

Abstract

We consider holomorphic Poisson-BF theory on twistor space. Classically, this describes self-dual Einstein gravity on space-time, but at the quantum level it is plagued by an anomaly. The anomaly corresponds to the fact that integrability of the self-dual vacuum Einstein equations does not survive in self-dual quantum gravity. We compute the anomaly polynomials in the Poisson-BF theory, as well as in this theory coupled to a holomorphic BF theory on twistor space describing self-dual Yang-Mills. We show that all anomalies may be cancelled by further coupling to a twistor field representing a type of axion on space-time. When the twistor anomalies are cancelled, all $n\geq4$-pt amplitudes vanish and integrability is restored.