Reconciling Grand Unification with Strings by Anisotropic Compactifications

TL;DR

This paper investigates gauge coupling unification in heterotic string models with anisotropic orbifolds, revealing specific scale hierarchies necessary for unification and predicting proton decay lifetimes within experimental reach.

Contribution

It demonstrates that gauge coupling unification requires the exotic mass scale to be much lower than the compactification scale in anisotropic orbifold models.

Findings

Unification is only possible if $ extrm{m}_{ex} \,\ll\, \textrm{m}_c$

Approximately 10% of parameter space predicts proton lifetimes between 10^{33} and 10^{36} years

Most parameter space yields proton decay rates below current experimental bounds

Abstract

We analyze gauge coupling unification in the context of heterotic strings on anisotropic orbifolds. This construction is very much analogous to effective 5 dimensional orbifold GUT field theories. Our analysis assumes three fundamental scales, the string scale, $\mstring$, a compactification scale, $\mc$, and a mass scale for some of the vector-like exotics, $\mex$; the other exotics are assumed to get mass at $\mstring$. In the particular models analyzed, we show that gauge coupling unification is not possible with $\mex = \mc$ and in fact we require $\mex \ll \mc \sim 3 \times 10^{16}$ GeV. We find that about 10% of the parameter space has a proton lifetime (from dimension 6 gauge exchange) $10^{33} {\rm yr} \lesssim\tau(p\to \pi^0e^+) \lesssim 10^{36} {\rm yr}$. The other 80% of the parameter space gives proton lifetimes below Super-K bounds. The next generation of proton decay experiments should be sensitive to the remaining parameter space.