Double copy map for double field theory on an arbitrary constant background

Double field theory (DFT) can be constructed up to third order as the double copy of Yang-Mills theory. In this construction, one starts with Yang-Mills theory on Minkowski space and the resulting DFT action is also defined on Minkowski space. In this work, I extend this double copy procedure to obtain a DFT action on a constant DFT background starting from two Yang-Mills actions constructed around nontrivial background gauge fields on Minkowski space.