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.

Automated summary

In this article, we study the target space theory of bosonic and heterotic string theory compactified to three dimensions at first order in α'. We use a formulation that is manifestly T duality invariant under O(d, d, R) with d = 23 and d = 7, respectively. Although the two-derivative supergravity exhibits a symmetry enhancement to the U duality group O(d + 1, d + 1), the continuous group is 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.