Statistics of M theory Vacua

TL;DR

The work analyzes vacuum statistics for M-theory compactifications on G2 manifolds with fluxes and for Freund-Rubin vacua, contrasting them with Type IIB flux landscapes. It shows that large volumes are strongly suppressed in G2 ensembles, and that cosmological-constant distributions are non-uniform and typically disfavor tiny Λ when many moduli are present; non-supersymmetric vacua dominate and SUSY breaking is usually at a high scale. The authors develop both general, model-independent results and an exactly solvable Kahler-potential class, revealing that vacua are distributed uniformly over moduli space (for SUSY cases) but with volume-driven suppression, and that metastable AdS vacua are plentiful while all dS vacua tend to be unstable. These findings highlight qualitative differences from IIB statistics and underscore the importance of constraints and ensemble choice in landscape predictions. The work points to avenues for refining ensembles, incorporating environmental criteria, and exploring implications for low-energy SUSY and phenomenology within M-theory frameworks.

Abstract

We study the vacuum statistics of ensembles of M theory compactifications on G_2 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 G_2 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.

Figures (7)

• Figure 1: Left: Lattice of vacua in $(k,N)$-space. The green solid lines have constant $V$ and the red dashed lines constant $\Lambda^{-1}$. Both are increasing with $N$ and $k$. Right: Vacua mapped to $(V,\Lambda^{-1})$-space with $V \leq 200,\Lambda^{-1} \leq 2000$. The lower and upper boundaries correspond to $k=1$ resp. $N=1$.
• Figure 2: Left: $E$ as a function of $A \equiv \vec{a}\cdot\vec{m}$. Here $E(-7/3)=3$ and $E(7/3)=-9/25$. Right: dependence of $\tilde{\Lambda}$ on $A$. At $A=-7/3$, $\tilde{\Lambda} \approx 10^{-3}$, and at $A=7/3$, $\tilde{\Lambda} \approx -13$. The divergence at $A=-1/3$ is due to the vanishing of the volume there.
• Figure 3: Distribution of $A$ values for $a_i=7n/3$, $n=50$.
• Figure 4: Dependence of $\tilde{V}_X^{\rm max}$ on $A$. At $A=7/3$, $\tilde{V}_X^{\rm max} = (3/5)^{7/3} \approx 0.3$, at $A=-7/3$, $\tilde{V}_X^{\rm max} = 3^{7/3} \approx 13$, and the zero is at $A=-1/3$.
• Figure 5: Density plot of the joint distribution of AdS vacua over $V_X$ and $\Lambda$, for $c_2=100$, $n=20$.