Symmetry enhancement interpolation, non-commutativity and Double Field Theory

We present a moduli dependent target space effective field theory action for (truncated) heterotic string toroidal compactifications. When moving continuously along moduli space, the stringy gauge symmetry enhancement-breaking effects, which occur at particular points of moduli space, are reproduced. Besides the expected fields, originating in the ten dimensional low energy effective theory, new vector and scalar fields are included. These fields depend on “double periodic coordinates” as usually introduced in Double Field Theory. Their mode expansion encodes information about string states, carrying winding and KK momenta, associated to gauge symmetry enhancements. It is found that a non-commutative product, which introduces an intrinsic non-commutativity on the compact target space, is required in order to make contact with string theory amplitude results.