A Review of Distributions on the String Landscape

TL;DR

This review explores the statistical distribution of string vacua properties, including moduli stabilization, parameter distributions, and phenomenological implications, to understand the landscape's structure and its relevance to observable physics.

Contribution

It provides a comprehensive overview of flux vacua counting techniques, distribution analyses, and phenomenological considerations in the string landscape, highlighting new insights into vacua finiteness and viability.

Findings

Distribution of cosmological constant analyzed

Finiteness of viable vacua discussed

Implications for phenomenology explored

Abstract

We review some basic flux vacua counting techniques and results, focusing on the distributions of properties over different regions of the landscape of string vacua and assessing the phenomenological implications. The topics we discuss include: an overview of how moduli are stabilized and how vacua are counted; the applicability of effective field theory; the uses of and differences between probabilistic and statistical analysis (and the relation to the anthropic principle); the distribution of various parameters on the landscape, including cosmological constant, gauge group rank, and SUSY-breaking scale; "friendly landscapes"; open string moduli; the (in)finiteness of the number of phenomenologically viable vacua; etc. At all points, we attempt to connect this study to the phenomenology of vacua which are experimentally viable.