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

TL;DR

This paper proves that Hodges' graviton MHV amplitude formula can be derived from an $Lw_{1+ abla}$ Ward identity on the celestial sphere, revealing a new recursion relation unrelated to BCFW and using the matrix-tree theorem.

Contribution

It introduces a novel Ward identity that generates Hodges' determinant, providing a new recursive approach to Einstein gravity amplitudes.

Findings

Hodges' formula is generated by an $Lw_{1+ abla}$ Ward identity.

A new recursion relation for graviton amplitudes is established.

The proof employs the matrix-tree theorem.

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.