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 five-dimensional orbifold grand unified theory field theories. Our analysis assumes three fundamental scales: the string scale M_S, a compactification scale M_C, and a mass scale for some of the vectorlike exotics M_EX; the other exotics are assumed to get mass at M_S. In the particular models analyzed, we show that gauge coupling unification is not possible with M_EX=M_C, and in fact we require M_EX«M_C~3×10^16 GeV. We find that about 10% of the parameter space has a proton lifetime (from dimension six gauge exchange) 10^33 yr = p^0 e^+) <= 10^36 yr. The other 80% of the parameter space gives proton lifetimes below Super-Kamiokande bounds. The next generation of proton decay experiments should be sensitive to the remaining parameter space