AdS vacua from dilaton tadpoles and form fluxes

We describe how unbounded three--form fluxes can lead to families of $AdS_3 \times S_7$ vacua, with constant dilaton profiles, in the $USp(32)$ model with "brane supersymmetry breaking" and in the $U(32)$ 0'B model, if their (projective--)disk dilaton tadpoles are taken into account. We also describe how, in the $SO(16) \times SO(16)$ heterotic model, if the torus vacuum energy $\Lambda$ is taken into account, unbounded seven--form fluxes can support similar $AdS_7 \times S_3$ vacua, while unbounded three--form fluxes, when combined with internal gauge fields, can support $AdS_3 \times S_7$ vacua, which continue to be available even if $\Lambda$ is neglected. In addition, special gauge field fluxes can support, in the $SO(16) \times SO(16)$ heterotic model, a set of $AdS_n\times S_10-n$ vacua, for all $n=2,..,8$. String loop and $\alpha'$ corrections appear under control when large form fluxes are allowed.