Weakly constrained double field theory: the quartic theory

Double field theory was originally introduced as the subsector of closed string field theory on a toroidal background given by the massless fields together with all their massive Kaluza-Klein and winding modes. These massive modes are encoded in the dependence of the massless fields on doubled toroidal coordinates, subject to the so-called 'weak constraint'. This theory was constructed by Hull and Zwiebach in 2009 to cubic order in fields, but due to the weak constraint it is a highly non-trivial problem to extend this to quartic and higher order. In this letter we announce and outline the construction of weakly constrained double field theory to quartic order, in which all coordinates are toroidal and doubled. To this end we use the framework of homotopy algebras and obtain double field theory as a double copy of the kinematic homotopy algebra of Yang-Mills theory.