Universal properties of type IIB and F-theory flux compactifications at large complex structure

We consider flux compactifications of type IIB string theory and F-theory in which the respective superpotentials at large complex structure are dominated by cubic or quartic terms in the complex structure moduli. In this limit, the low-energy effective theory exhibits universal properties that are insensitive to the details of the compactification manifold or the flux configuration. Focussing on the complex structure and axio-dilaton sector, we show that there are no vacua in this region and the spectrum of the Hessian ;matrix is highly peaked and consists only of three distinct eigenvalues (0, 2m(3/2)(2) and 8m(3/2)(2)), independently of the number of moduli. We briefly comment on how the inclusion of Kahler moduli affect these findings. Our results generalise those of Brodie & Marsh [1], in which these universal properties were found in a subspace of the large complex structure limit of type IIB compactifications.