F-theory flux vacua at large complex structure

Understand

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.