Distributions of nonsupersymmetric flux vacua

TL;DR

This paper investigates the distribution of nonsupersymmetric flux vacua in type IIB string theory, revealing how eigenvector structures of the superpotential's second derivatives influence supersymmetry breaking scales, using random matrix theory.

Contribution

It introduces a novel approach linking flux vacua distributions to eigenvector properties of superpotential matrices, employing the CI ensemble from mesoscopic physics.

Findings

Eigenvector structure of the superpotential matrix influences vacua distribution.

Features of the CI ensemble determine key aspects of supersymmetry breaking.

Examples show factors favoring low or high scale supersymmetry breaking.

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.