𝑈 duality and 𝛼′ corrections in three dimensions

We consider the target space theory of bosonic and heterotic string theory to first order in 𝛼′ 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 𝛼′ correction. We revisit this observation by computing the full effective actions in three dimensions to first order in 𝛼′ 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.