The classical double copy of noncommutative Yang-Mills yields a theta-squared-corrected cubic double field theory action whose pure gravity limit is Einstein-Hilbert plus Riemann-cubed terms in D=4 transverse-traceless gauge.
Construction of non-Abelian gauge theories on noncommutative spaces
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We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with aconstant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories.
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From noncommutative Yang-Mills to noncommutative gravity through a classical double copy map
The classical double copy of noncommutative Yang-Mills yields a theta-squared-corrected cubic double field theory action whose pure gravity limit is Einstein-Hilbert plus Riemann-cubed terms in D=4 transverse-traceless gauge.