Reconciling Grand Unification with Strings by Anisotropic Compactifications

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.