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

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.

61 pages, 11 figures; v2: clarifications added, typos corrected; v3: published in JHEP

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• Lectures on Celestial Amplitudes
• Holographic Symmetry Algebras for Gauge Theory and Gravity
• Generating Tree Amplitudes in N=4 SYM and N=8 SG
• Taming Tree Amplitudes In General Relativity
• Celestial holography meets twisted holography: 4d amplitudes from chiral correlators
• Twistor Actions for Self-Dual Supergravities
• On Effective Field Theories with Celestial Duals
• Loop-level gluon OPEs in celestial holography
• Flat Self-dual Gravity
• The 4d/2d correspondence in twistor space and holomorphic Wilson lines
• The Twelve-Graviton Next-to-MHV Amplitude from Risager's Construction

Cited by in corpus (10)

• The Celestial Chiral Algebra of Self-Dual Gravity on Eguchi-Hanson Space
• From Moyal deformations to chiral higher-spin theories and to celestial algebras
• Deforming Soft Algebras for Gauge Theory
• Celestial Locality and the Jacobi Identity
• All-order celestial OPE in the MHV sector
• Celestial amplitudes in an ambidextrous basis
• All-order celestial OPE from on-shell recursion
• Celestial $s{w}_{1+\infty }$ algebra in Einstein-Yang-Mills theory
• One-loop corrections to the celestial chiral algebra from Koszul Duality
• Asymptotic Higher Spin Symmetries II: Noether Realization in Gravity