The Distribution of Vacua in Asymptotic Flux Compactification of Type IIB / F-Theory

Abstract

Much of recent research in string theory has revolved around the complexity of the landscape of inequivalent vacua which may describe the world we observe. In this work, we review the emergence of this landscape from the perspective of flux compactifications of F-theory and discuss its statistical description in terms of the index density of supersymmetric flux vacua following the many works of Douglas et al. We then proceed to analyze the behaviour of the index density near singular loci in the complex structure moduli space using asymptotic Hodge theory. In all single parameter limits, we obtain a universal asymptotic behaviour of the index density which is integrable, providing evidence for the finiteness of string theory flux vacua. We are also able to extend our analysis to some multi-parameter limits and point the reader to possible methods to describe the full set of limits.