On the extension of double copy procedure to higher derivative double field theory

Double field theory (DFT) can be constructed from the color-kinematic double copy of Yang- Mills theory. In a recent work, this construction has been extended to higher-derivative terms, starting from the four-derivative extension of Yang-Mills theory, to obtain a conformally invariant DFT action up to the third order. Here, I attempt to extend this idea by introducing a method, inspired by the background independent formulation of DFT, to obtain third order higher derivative terms directly from the second order higher derivative terms. The third-order terms I obtain do not match those obtained directly from the double-copy map. A clear understanding of this mismatch can give valuable information about the double copy procedure for DFT, its relation to background independence, and the conformal symmetry in double configuration space.