Quantizing the non-linear graviton

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 $n\ge 4$-pt amplitudes vanish and integrability is restored.

70 pages, 12 figures; v2: clarifications added, typos corrected; v3: published in CIMP

References in corpus (6)

• Holographic Symmetry Algebras for Gauge Theory and Gravity
• Twistor Actions for Self-Dual Supergravities
• Celestial operator products from the worldsheet
• The Chern-Simons Origin of Superstring Integrability
• Flat Self-dual Gravity
• Positive helicity Einstein-Yang-Mills amplitudes from the Double Copy

Cited by in corpus (6)

• Integrable Deformations from Twistor Space
• Gauging The Diamond: Integrable Coset Models from Twistor Space
• Celestial Quantum Error Correction II: From Qudits to Celestial CFT
• Holomorphic field theories and higher algebra
• Integrable models from 4d holomorphic BF theory
• The One-Loop QCD $\beta$-Function as an Index