Heterotic/F-theory duality and Narasimhan-Seshadri equivalence

Finding the F-theory dual of a Heterotic model with Wilson-line symmetry breaking presents the challenge of achieving the dual Z(2)-action on the F-theory model in such a way that the Z(2)-quotient is Calabi-Yau with an Enriques GUT surface over which SU (5)(gauge) symmetry is maintained. We propose a new way to approach this problem by taking advantage of a little-noticed choice in the application of Narasimhan-Seshadri equivalence between real E-8-bundles with Yang-Mills connection and their associated complex holomorphic E-8(C)-bundles, namely the one given by the real outer automorphism of E-8(C) by complex conjugation. The triviality of the restriction on the compact real form E-8 allows one to introduce it into the Z(2)-action, thereby restoring E-8- and hence SU (5)(gauge)-symmetry on which the Wilson line can be wrapped.