Supersymmetry Breaking in the Anthropic Landscape

TL;DR

The paper examines the Banks–Dine–Gorbatov critique of the anthropic landscape by applying Bayes’ theorem to compare the likelihood of different SUSY-breaking scales $M$ under anthropic constraints on $\lambda$ and $\mu$. It shows that the posterior probability depends on both a potentially strong radiative bias $P(\lambda,\mu|M) \sim M^{-6}$ and the landscape prior $P(M)$, which may suppress or enhance low-$M$ regions depending on the distribution of SUSY-breaking sectors. By analyzing a KKLT-like setup with multiple throats, it demonstrates how combinatorial factors can tilt the measure toward higher $M$, challenging the notion that anthropic selection alone favors low-energy SUSY. The Note Added surveys subsequent work by Denef, Douglas, and Florea, which refines the probabilistic framework and suggests that the conclusions about low- vs high-scale SUSY breaking depend sensitively on the assumed distributions of $\lambda$ and the overall landscape measure, highlighting the need for quantitative treatment of the measure in string vacua.

Abstract

In this paper I attempt to address a serious criticism of the ``Anthropic Landscape" and "Discretuum" approach to cosmology, leveled by Banks, Dine and Gorbatov. I argue that in this new and unfamiliar setting, the gauge Hierarchy may not favor low energy supersymmetry. In a added note some considerations of Douglas which substantially strengthen the argument are explained.