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 ρ A ρ B up to exponentially-suppressed terms, with ρ depending on the fluxes and axions and Z on the saxions. We provide explicit, general expressions for Z and ρ, 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 flux which is bounded. In the first and most generic one, the saxion vevs are bounded from above by a power of N flux . In the second their vevs may be unbounded and N 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.

Large complex structure flux vacua of IIB and the Tadpole Conjecture

“…In this note we would like to demonstrate that taking the estimates of [3] at face value and combining them with the results of [2] on IIB vacua indicates that also in the second class of vacua in [2] N flux cannot be made arbitrarily small and scales approximately linear with n moduli , in agreement with (1).…”

“…The IIB2 scenario of [2] This setup considers fluxes where the only non-vanishing flux quanta are given by…”

“…We proceed by summarizing a few elementary facts on flux compactifications in the large complex structure limit of IIB. Afterwards, we collect the relevant results of [2] and [3] and show that when combined they support the tadpole conjecture, even when taking polynomial corrections to the prepotential into account.…”

“…Recently, the authors of [2] provided a detailed analysis of F-theory and IIB flux compactifications at large complex structure and suggested a potential counter example to the above conjecture. They found two classes of vacua which appear to have qualitatively different behavior with respect to (1).…”

“…The results found there are not only compatible with the tadpole conjecture but suggest an even more dramatic, polynomial scaling behavior of N flux with n moduli . Yet, the analysis in [3] differs from the one in [2] as it does not include certain correction terms which were crucial for the construction of the potential counter example of (1).…”