Some new aspects of Heterotic - F-theory duality

Here, we used a notation of effective theory with SU(5)GUT symmetry and N = 1 supersymmetry. Simple perturbative Yang–Mills interactions of open strings of Type IIA / IIB string theory may be able to give rise to the latter, but the up-type Yukawa couplings with SU(5)GUT indices contracted by an epsilon tensor are hard to be generated. Heterotic E8×E′ 8 string theory, G2-holonomy compactification of 11-dimensional supergravity and F-theory compactification, however, are capable of generating both types of Yukawa couplings.