Statistical analysis of the supersymmetry breaking scale

TL;DR

Douglas presents a statistical landscape framework to assess which SUSY-breaking scales are favored among string/M theory vacua. By modeling the joint distribution of F- and D-term breaking parameters and enforcing a near-zero cosmological constant with a delta constraint, he argues that the distribution of the high-energy scale $\hat{\Lambda}$ is broadly uniform and largely uncorrelated with SUSY breaking, leaving the SUSY-breaking scale distribution governed by the structure of the breaking parameter space. In high-dimensional breaking spaces, the total SUSY-breaking scale tends to grow toward larger values, $d(M_{susy}^2) \propto (M_{susy}^2)^{2n_F+n_D-1}$, though conifold enhancements and antibrane contributions can realize hierarchically small scales; whether low- or high-scale SUSY is realized depends on whether the observable-sector breaking is driven by a single parameter or by a sum of several independent positive contributions, with cutoff and stability constraints shaping the outcome. Overall, the framework clarifies how the landscape's counting and parameter structure translate into qualitative expectations for SUSY-breaking scales and highlights paths toward falsifiable predictions as vacua statistics improve.

Abstract

We discuss the question of what type and scale of supersymmetry breaking might be statistically favored among vacua of string/M theory, building on comments in Denef and Douglas, hep-th/0404116.