Observations on the Space of Four Dimensional String and $M$ theory Vacua

TL;DR

This paper explores the complex landscape of four-dimensional string and M-theory vacua, emphasizing their disconnected nature, the importance of classifying different components, and proposing criteria to exclude certain vacua based on supersymmetry perturbations.

Contribution

It identifies the disconnected structure of vacua space and suggests methods to classify and potentially exclude certain vacua, advancing understanding of the string theory landscape.

Findings

Vacua form disconnected components with distinct universality classes.

Statistical distribution calculations must account for these separate components.

Proposes an argument to exclude vacua that are small perturbations of supersymmetric AdS4.

Abstract

The space of four dimensional string and $M$ theory vacua with non-Abelian gauge symmetry, chiral fermions and unbroken supersymmetry beyond the electroweak scale appears to be a disconnected space whose different components represent distinct universality classes of vacua. Calculating statistical distributions of physical observables a la Douglas therefore requires that the distinct components are carefully accounted for. We highlight some classes of vacua which deserve further study and suggest an argument which may serve to rule out vacua which are small perturbations of supersymmetric $AdS_4$.