Generating Hodges' Graviton MHV Formula with an Lw_1+∞ Ward Identity

2025/06/05 by Alfredo Guevara, Guevara, Alfredo, Elizabeth Himwich +3
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories

paper · pdf · doi:10.48550/arxiv.2506.05460

openalex publication_date 2025/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Hodges' formula expresses the tree-level all-multiplicity Einstein gravity MHV amplitude as a matrix determinant. In this work, we prove that Hodges' determinant is generated by an Lw_1+∞ Ward identity on the celestial sphere. The Ward identity takes the form of a recursion relation that has not previously appeared in the literature and is unrelated to BCFW. The proof makes use of the matrix-tree theorem.

Citations

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Related

• A simple formula for gravitational MHV amplitudes
• The KLT Relation from the Tree formula and Permutohedron
• Gravity MHV amplitudes via Berends-Giele currents
• Proof of the graviton MHV formula using Plebański's second heavenly equation
• Computing NMHV Gravity Amplitudes at Infinity