Strings at the Intermediate Scale, or is the Fermi Scale Dual to the Planck Scale?

TL;DR

The paper proposes identifying the string scale with the intermediate scale, $M_s=\sqrt{M_W M_{Planck}}$ (≈ $10^{11}$ GeV), to naturally generate the observed hierarchy without tiny dimensionless inputs. In a weakly-coupled Type-I open-string setup with the SM on a SUSY 3-brane and SUSY breaking in a distant hidden 3-brane, the hierarchy follows from a modest $M_c/M_s$ via $M_W/M_{Planck}=\frac{1}{2}\alpha_{GUT}^2 (M_c/M_s)^6$, with $M_s$ providing a bridge between the weak and Planck scales. The framework yields several phenomenological benefits, including logarithmic gauge-coupling unification at $M_s$, invisible axions with a PQ scale around $M_s$, and potentially viable neutrino masses, along with implications for proton stability and cosmology. A dual-like relation $M_W=1/(\alpha' M_{Planck})$ with $\alpha'\sim 1/M_s^2$ hints at a deeper link between the Fermi and Planck scales, suggesting intermediate-scale string theory could be phenomenologically rich and testable.

Abstract

We show that if the string scale is identifed with the intermediate scale, $M_s=\sqrt{M_W M_{Planck}} \sim 10^{11}$ GeV, then the notorious hierarchy, $M_W/M_{Planck} \sim 10^{-16}$, can be explained using only $M_c/M_s \sim 0.01 \sim α_{GUT} $ as small input parameters, where $M_c$ is the compactification scale. This is possible for weakly-coupled Type-I open-string vacua if the observed world is assumed to live in an N=1 supersymmetric 3-brane sector coupled to a separate, hidden, 3-brane world which breaks supersymmetry, because for such a model $M_W/M_{Planck} = 1/2 α_{GUT}^2 (M_c/M_s)^6$. We discuss some of the phenomenological issues presented by such an intermediate-scale string, showing that its benefits include: (i) the possibility of logarithmic gauge-coupling unification of the SM couplings at $M_s$; (ii) a natural axionic solution to the strong-CP problem with a phenomenologically-acceptable Peccei-Quinn scale; (iii) experimentally-interesting neutrino masses, and more.