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Generating Hodges' Graviton MHV Formula with an $Lw_{1+\infty}$ Ward Identity
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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.
Forward citations
Cited by 2 Pith papers
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Soft Algebras via Bulk Double Soft Limits
Bulk double soft limits of gravitational amplitudes fail to reproduce the recursive generation of higher-order soft theorems that celestial soft algebras suggest from the first three terms alone.
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Holographic symmetry algebra for the MHV sector revisited
In the MHV sector, the celestial symmetry algebra is a semidirect product of w_{1+∞} (or S) with an infinite Abelian algebra, whose null states supply the two missing KZ equations.
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