Unification with Low String Scale

Abstract

I argue that in open-string theory with hierarchically small (or large) extra dimensions, gauge groups can unify naturally with logarithmically-running coupling constants at the high Kaluza-Klein (or string-winding) scale. This opens up the possibility of rescuing the standard logarithmic unification at $M_U\sim 10^{15-18}$ GeV even if the fundamental-string scale is much lower, at intermediate or possibly even electroweak scales. I also explain, however, why a low type-I string scale may not suffice to obliterate the ultraviolet problems usually associated with the gauge hierarchy.

Comments: 6 pages, uses harvmac. Two minor changes. Final version to appear in JHEP