U duality and a' corrections in three dimensions

We consider the target space theory of bosonic and heterotic string theory to first order in & alpha;' compactified to three dimensions, using a formulation that is manifestly T duality invariant under O(d, d, R) with d = 23 and d = 7, respectively. While the two-derivative supergravity exhibits a symmetry enhancement to the U duality group O(d + 1, d + 1), the continuous group is known to be broken to O(d, d, R) by the first & alpha;' correction. We revisit this observation by computing the full effective actions in three dimensions to first order in & alpha;' by dualizing the vector gauge fields. We give a formally O(d + 1, d + 1) invariant formulation by invoking a vector compensator, and we observe a chiral pattern that allows one to reconstruct the bosonic action from the heterotic action. Furthermore, we obtain a particular massive deformation by integrating out the external B field. This induces a novel Chern-Simons term based on composite connections that, remarkably, is O(d + 1, d + 1) invariant to leading order in the deformation parameter.