Mirage gauge coupling unification

TL;DR

The paper investigates how gauge coupling unification can survive a low string scale in explicit Type IIB orientifold vacua by exploiting moduli-dependent corrections to gauge couplings. It shows that anomalous U(1) Fayet-Iliopoulos terms induce modulus dependence in the gauge kinetic function that, together with sigma-model anomaly cancellation, yields effective running up to a virtual scale $M_X$ rather than the string scale. The key result is that the observed unification can be a mirage: the actual running stops at the string scale, but the corrections emulate running to $M_X$. The author demonstrates this mechanism in a simple MSSM extension with $M_X$ chosen to reproduce MSSM unification, requiring $M_{string}\sim 10^{11}$ GeV and $M_c\sim 10^{9}$ GeV, aligning with independent arguments for an intermediate string scale. The work highlights a potential general route to low string scales that preserves precision gauge coupling unification and motivates further model-building and phenomenological exploration.

Abstract

We use compact D=4, N=1, Type IIB orientifolds as a testing ground for recent ideas about precocious gauge coupling unification and a low energy string scale. We find that certain such orientifolds have the interesting property that gauge couplings receive moduli-dependent corrections which mimic the effect of field theoretical logarithmic running. The effective cut-off scale for the logarithmic correction is not $M_{string}$ but rather $M_X=\sqrtαM_{Planck}M_c/M_{string}$, where $M_c$ is the compactification scale. Thus there is just normal logarithmic running up to $M_{string}$ and extra moduli dependent corrections which behave as if there was further running to a higher virtual scale $M_X$. In this mechanism a prominent role is played by anomalous U(1)'s with moduli dependent Fayet-Iliopoulos terms. A vanishing FI-term fixes the modulus dependence of the corrected gauge coupling. We discuss possible ways to implement this mechanism in the context of a simple extension of the MSSM.

Figures (1)

• Figure 1: Mirage unification in the MSSM. The couplings run up to the string scale $M_s\approx 10^{11} GeV$. The compactification scale $M_c\approx 10^9 GeV$ creates no new KK thresholds, since the gauge fields live on 3-branes. The couplings have an apparent unification at the virtual scale $M_X=\sqrt{\frac{2}{\alpha}} M_s^3/M_c^2$. From low energies everything looks like if there was a field theory desert in between $M_W$ and $M_X$.