U-duality and $\alpha'$ corrections in three dimensions

TL;DR

This paper investigates the effects of first-order $mbda'$ corrections on U-duality and T-duality symmetries in three-dimensional string theories, revealing invariant formulations and novel deformations.

Contribution

It provides a formal ${ m O}(d+1,d+1)$ invariant formulation of the effective action with $mbda'$ corrections and introduces a new massive deformation with a Chern-Simons term.

Findings

Reconstruction of the bosonic action from the heterotic action.

Identification of a massive deformation with a Chern-Simons term.

Demonstration of ${ m O}(d+1,d+1)$ invariance at leading order.

Abstract

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 ${\rm O}(d,d,\mathbb{R})$ with $d=23$ and $d=7$, respectively. While the two-derivative supergravity exhibits a symmetry enhancement to the U-duality group ${\rm O}(d+1,d+1)$, the continuous group is known to be broken to ${\rm O}(d,d,\mathbb{R})$ 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 ${\rm O}(d+1,d+1)$ 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 ${\rm O}(d+1,d+1)$ invariant to leading order in the deformation parameter.