Heterotic-F-theory duality with Wilson line symmetry-breaking

Abstract

We begin with an E8 x E8 Heterotic model broken to an SU(5)gauge and a mirror SU(5)gauge, where one SU(5) and its spectrum is identified as the visible sector while the other can be identified as a hidden mirror world. In both cases we obtain the minimal supersymmetric standard model spectrum after Wilson-line symmetry-breaking enhanced by a low energy R-parity enforced by a local (or global) U(1)x-symmetry. Using Heterotic/F-theory duality, we show how to eliminate the vector-like exotics which were obtained in previous constructions. In these constructions, the Calabi-Yau [CY] four-fold was defined by an elliptic fibration with section over a base B3 and a GUT surface given by K3/ℤ2 = Enriques surface. In the present paper we construct a quotient CY four-fold fibered by tori with two elliptic structures given by a pair of sections fibered over the Enriques surface. Using Heterotic/F-theory duality we are able to define the cohomologies used to derive the massless spectrum. Our model for the 'correct' F-theory dual of a Heterotic model with Wilson-line symmetry-breaking builds on prior literature but employs the stack-theoretic version of the dictionary between the Heterotic semi-stable Es-bundles with Yang-Mills connection and the dP9-fibrations used to construct the F-theory dual.