Unification with extra dimensions

Abstract

We study the gauge unification in higher-dimensional orbifold field theory which is known to be useful for constructing a natural model of gauge unification which is free from difficulties that the conventional 4 dimensional grand unified theories suffer from. We begin with examining the gauge coupling renormalization in orbifold field theory in the context of 4 dimensional effective supergravity. We obtain the 1-loop correction to the gauge coupling in generic 5 dimensional super-Yang-Mills models defined on a slice of AdS5 preserving N=1 supersymmetry. We also calculate the full 1-loop corrections to the low energy coupling of bulk gauge boson in AdS5 due to 5D general scalar, fermion and vector fields with arbitrary $Z_2＼times Z^``_2$ orbifold boundary condition. Using these results, we derive the Kaluza-Klein threshold corrections to low energy gauge coupling due to quasi-localized matter fields which generate hierarchical 4 dimensional Yukawa couplings. Applying the results to 5 deminsional orbifold GUT``s, we discuss the conditional for a 5 dimensional grand unified theory to generate hierarchical Yukawa coupling without spoiling successful gauge coupling unification.