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Graphs, determinants and gravity amplitudes
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abstract
We apply the matrix-tree theorem to establish a link between various diagrammatic and determinant expressions, which naturally appear in scattering amplitudes of gravity theories. Using this link we are able to give a general graph-theoretical formulation for the tree-level maximally-helicity-violated gravity amplitudes. Furthermore, we use the link to prove two identities for half-soft functions of gravity amplitudes. Finally we recast the diagrammatic formulation of one-loop rational part of $\mathcal{N}=4$ supergravity into a matrix form.
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Cited by 1 Pith paper
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Generating Hodges' Graviton MHV Formula with an $Lw_{1+\infty}$ Ward Identity
Hodges' all-multiplicity graviton MHV determinant is exactly generated by a one-particle recursion that takes the form of an Lw_{1+∞} Ward identity.
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