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The Kawai–Lewellen–Tye (KLT) relations derived from string theory tell us that perturbative gravity amplitudes are the “square” of the corresponding amplitudes in gauge theory. Starting from the light-cone Lagrangian for pure gravity we make these relations manifest off-shell, for three- and four-graviton vertices, at the level of the action.
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Ananth et al. (2007) studied this question.
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