STRING UNIFICATION SCALE AND THE HYPER-CHARGE KAC-MOODY LEVEL IN THE NONSUPERSYMMETRIC STANDARD MODEL

The string theory predicts the unification of the gauge couplings and gravity. The minimal supersymmetric Standard Model, however, gives the unification scale similar to 2 x 10(16) GeV which is significantly sm aller than the string scale similar to 5 x 10(17) GeV of the weak coup ling heterotic string theory. We study the unification scale of the no n-supersymmetric minimal Standard Model quantitatively at the two-loop level. We find that the unification scale should be at most similar t o 4 x 10(16) GeV and the desired Kac-Moody level of the hyper-charge c oupling should be 1.33 less than or similar to k(Y) less than or simil ar to 1.35. (C) 1998 Elsevier Science B.V.