Type IIB flux vacua and tadpole cancellation

We consider flux vacua for type IIB orientifold compactifications and study their interplay with the tadpole‐cancellation condition. As a concrete example we focus on $T^6$/$Z_2$ $\times$ $Z_2$, for which we find that solutions to the F‐term equations at weak coupling, large complex structure and large volume require large flux contributions. Such contributions are however strongly disfavored by the tadpole‐cancellation condition. We furthermore find that solutions which stabilize moduli in this perturbatively‐controlled regime are only a very small fraction of all solutions, and that the space of solutions is not homogenous but shows characteristic void structures and vacua concentrated on submanifolds. (© 2019 The Authors. Published by Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)