Distributions of nonsupersymmetric flux vacua
Frederik Denef, Michael R. Douglas
TL;DR
The paper reframes the problem of counting nonsupersymmetric flux vacua in type IIB on Calabi–Yau manifolds as an eigenvector problem for the second-derivative structure of the superpotential, leveraging a CI random-matrix ensemble to derive vacuum densities. It derives explicit density formulas, analyzes simple and generic multi-parameter IIb examples (including a one-modulus case and a T^6/ℤ_2^2 orbifold), and shows metastable nonsupersymmetric vacua are generically abundant with a universal correction factor linked to the SUSY-breaking sector. The authors also compare continuous-flux approximations to quantized fluxes and study the impact of D-terms, finding lifted SUSY vacua near conifold points can yield low-scale SUSY breaking under certain conditions, while generic F-breaking vacua are typically suppressed. Overall, the work identifies robust, generic features of vacuum statistics that influence naturalness questions and highlights both the potential and limitations of current landscape counting approaches.
Abstract
We continue the study of the distribution of nonsupersymmetric flux vacua in IIb string theory compactified on Calabi-Yau manifolds, as in hep-th/0404116. We show that the basic structure of this problem is that of finding eigenvectors of the matrix of second derivatives of the superpotential, and that many features of the results are determined by features of the generic ensemble of such matrices, the CI ensemble of Altland and Zirnbauer originating in mesoscopic physics. We study some simple examples in detail, exhibiting various factors which can favor low or high scale supersymmetry breaking.