F-theory flux vacua at large complex structure

Abstract: We compute the flux-induced F-term potential in 4d F-theory compactifications at large complex structure. In this regime, each complex structure field splits as an axionic field plus its saxionic partner, and the classical F-term potential takes the form $V = Z^{AB} \rho_A\rho_B$ up to exponentially-suppressed terms, with $\rho$ depending on the fluxes and axions and $Z$ on the saxions. We provide explicit, general expressions for $Z$ and $\rho$, and from there analyse the set of flux vacua, for an arbitrary number of fields. We identify two families of vacua with all complex structure fields fixed and a flux contribution to the tadpole $N_{\rm flux}$ which is bounded. In the first and most generic one, the saxion vevs are bounded from above by a power of $N_{\rm flux}$. In the second their vevs may be unbounded and $N_{\rm flux}$ is a product of two arbitrary integers, unlike what is claimed by the Tadpole Conjecture. We specialise to type IIB orientifolds, where both families of vacua are present, and link our analysis with several results in the literature. We finally illustrate our findings with several examples.