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We study a novel class of higher derivative theories for interacting masslessgravitons in Minkowski spacetime. These theories were first discussed by Walddecades ago, and are characterized by scattering amplitudes essentiallydifferent from general relativity and many of its modifications. We discussvarious aspects of these higher derivative theories, including the Lagrangianconstruction, violation of asymptotic causality, scattering amplitudes,non-renormalization, and possible implications on emergent gravitons fromcondensed matter systems.

Higher Derivative Theories for Interacting Massless Gravitons in Minkowski Spacetime