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arXiv · 2506.05460

Generating Hodges' Graviton MHV Formula with an $Lw_{1+\infty}$ Ward Identity

Alfredo Guevara·Elizabeth Himwich·Noah Miller
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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 $Lw_{1+\infty}$ 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.

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Alfredo Guevara, Elizabeth Himwich, Noah Miller. 2025-06-05. Generating Hodges' Graviton MHV Formula with an $Lw_{1+\infty}$ Ward Identity. https://arxiv.org/abs/2506.05460

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