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At the classical level, chiral gravity may be constructed as a consistent truncation of a larger theory called log gravity by requiring that left-moving charges vanish.
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J. M. Maldacena, “The large N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys. 2
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E. Ayon-Beato and M. Hassaine, “pp waves of conformal gravity with self-interacting source,” Annals Phys. 317
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2009
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2009
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