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Self-dual gravity is a diffeomorphism invariant theory in four dimensions that describes two propagating polarisations of the graviton and has a negative mass dimension coupling constant.
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D. Cangemi, “Selfduality and maximally helicity violating QCD amplitudes,” Int. J. Mod. Phys. A 12
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Z. Bern, L. J. Dixon, M. Perelstein and J. S. Rozowsky, “One loop n point helicity amplitudes in (selfdual) gravity,” Phys. Lett. B 444
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K. Krasnov, “One-loop beta-function for an infinite-parameter family of gauge theories,” JHEP 1503
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