Self-Dual Point and Unification

Abstract

We hypothesize that the vacuum is spontaneously shifted from the self-dual point in the moduli space, at which all dimensions are compact, and that the true vacuum results from the decompactification of the four space-time dimensions and remains in the vicinity of the self-dual point for extra dimensions. On the basis of our hypotheses we explore new types of the coupling unification which are not realized in the four-dimensional effective theory but in the framework of the higher dimensional theory. In the $SU(6)\times SU(2{)}_R$ string model, if the SU(6) gauge group lives in the world-volume of 9-branes and the $SU(2{)}_R$ in the world-volume of 5-branes, or {\it vice versa}, unification solutions can be found in the vicinity of the self-dual point.

Comments: 12 pages, latex, no figures, final version to appear in Prog. Theor. Phys. Vol. 102 (1999) No. 4