Heterotic de-Sitter Solutions

We classify all warped product de-Sitter backgrounds in heterotic supergravity, up to two loops. We find that warped $dS_n$ backgrounds, with $n\ge 3$, are $\mathbb{R}^{1,n}\times M_{9-n}$, where $M_{9-n}$ is a $(9-n)$-dimensional Riemannian manifold. Moreover, we establish that warped $dS_2$ backgrounds are $AdS_3\times M_7$, where $M_7$ is a 7-dimensional Riemannian manifold.