Branches of the landscape

Abstract

To cite this article: Michael Dine et al JHEP07(2005) Abstract: With respect to the question of supersymmetry breaking, there are three branches of the flux landscape. On one of these, if one requires small cosmological constant, supersymmetry breaking is predominantly at the fundamental scale; on another, the distribution is roughly flat on a logarithmic scale; on the third, the preponderance of vacua are at very low scale. A priori, as we will explain, one can say little about the first branch. The vast majority of these states are not accessible even to crude, approximate analysis. On the other two branches one can hope to do better. But as a result of the lack of access to branch one, and our poor understanding of cosmology, we can at best conjecture about whether string theory predicts low energy supersymmetry or not. If we hypothesize that are on branch two or three, distinctive predictions may be possible. We comment of the status of naturalness within the landscape, deriving, for example, the statistics of the first branch from simple effective field theory reasoning.

One in a billion: MSSM-like D-brane statistics

“…The first stack is therefore of the type (18) or (19), the second can also be of the form (20). In some cases, the Standard Model quantum numbers can also be realised on three stacks only at the cost of having no standard Yukawa couplings (which are not always realistic in the four stack models either).…”

The intermediate scale branch of the landscape

“…One can make reliable statements on this branch only for small supersymmetry breaking scale, m 3/2 ≪ M p . In this regime the distribution behaves, for small cosmological constant, Λ < Λ o , as [7,9] dm 3/2 P (m 3/2 ) = Λ o dm 2 3/2 m 10 3/2 .…”

“…The possible existence, in string theory, of an exponentially large number of stable and metastable vacua without supersymmetry or with N = 1 supersymmetry in four dimensions, the "landscape" [1,2,3,4], provides a realization of this idea. Much is already known about the statistics of these states [5,6,7,8,9], and it is possible to assess the tunings required to understand the values of parameters such as the cosmological constant and the weak scale. It is even possible to make some cautious statements about correlations which might lead to experimental predictions.…”

“…For nonsupersymmetric states, the situation is potentially quite different. The arguments of [7,9] establish criteria for the counting of local minima, but global questions are more challenging. The typical non-supersymmetric state with small, positive cosmological constant is surrounded (in the lattice of fluxes) by other states, presumably roughly half of which typically have negative cosmological constant.…”

“…States on the low energy branch arise when there is a (dynamically broken) Rsymmetry and supersymmetry. These states are inevitably less numerous than states without such symmetries [8,17,9], and recent studies have shown that this suppres-sion can be quite substantial [18,19]. One other troubling feature of this branch is that the vast majority of states have moduli, which are only fixed as a result of supersymmetry breaking.…”