Statistics of String vacua

TL;DR

The paper advocates a statistical, ensemble-based approach to the string theory landscape, arguing that the sheer number of potential vacua requires examining distributions of low-energy theories rather than single models. It develops concrete frameworks for counting and characterizing vacua, including a quiver/gauge-theory distribution for D-brane constructions and a rigorous counting of flux vacua in type IIb via an index integral constrained by tadpole cancellation. The results indicate an enormous but structured landscape, with estimates showing exponential growth in the number of flux vacua and a near-uniform distribution of small cosmological constants, while KKLT-style stabilization and dualities shape the viable regions of moduli space. The analysis highlights both the challenge and opportunity: vast numbers threaten predictivity, but well-defined statistical tests could still single out viable, testable vacua when combined with phenomenological constraints.

Abstract

We give an introduction to the statistical approach to studying vacua of string/M theory, and discuss recent results of Ashok and Douglas on counting supersymmetric flux vacua in type IIb Calabi-Yau compactification. To appear in the proceedings of the 2003 String Phenomenology workshop in Durham, UK.