Statistics of M-theory vacua

Abstract

We study the vacuum statistics of ensembles of <i>M</i> theory compactifications on G₂ holonomy manifolds with fluxes, and of ensembles of Freund-Rubin vacua. We discuss similarities and differences between these and Type IIB flux landscapes. For the G₂ ensembles, we find that large volumes are strongly suppressed, and for both, unlike the IIB case, the distribution of cosmological constants is non-uniform. We also argue that these ensembles typically have exponentially more non-supersymmetric than supersymmetric vacua, and show that supersymmetry is virtually always broken at a high scale.