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We construct the pure gravity Becchi-Rouet-Stora-Tyutin (BRST)Einstein-Hilbert Lagrangian, to cubic order, using the BRST convolution productof two Yang-Mills theories, in conjunction with the Bern-Carrasco-Johansson(BCJ) double-copy.

The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order