Background independent higher derivative double field theory action

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 with an expectation to obtain a conformally invariant DFT action up to the third order. Here, I attempt to extend this higher-derivative DFT action for all orders in a manifestly background-independent way starting from the second order terms. The third order terms I obtained do not match the third order terms 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.