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.
Highlights
1.1 The physics Supersymmetric grand unified theories [SUSY GUTs] [17, 18, 29] have many nice properties
Using Heterotic/F -theory duality, we show how to eliminate the vector-like exotics which were obtained in previous constructions
The purpose of this paper is to present a model for Heterotic/F -theory duality in which SU(5) symmetry is broken by Wilson lines
Summary
1.1 The physics Supersymmetric grand unified theories [SUSY GUTs] [17, 18, 29] have many nice properties. We emphasize that the presence of some kind of vector-like exotic matter is not a specific issue with this Enriques model but rather a general property of any model that breaks SU(5)GUT → SU(3) × SU(2) × U(1)Y with a flat U(1)Y bundle on a holomorphic surface SGUT We note that this derivation is, only valid if the F -theory is compactified on a CY 4-fold with section. A very novel feature of the model is that it contains a twin/mirror SU(5) symmetry broken to a mirror SM with three families of mirror quarks and leptons and a pair of mirror Higgs multiplets.1 This is a direct consequence of the fact that the GUT surface, SG∨UT = Enriques, is a branched ( irreducible) double cover of the base B2. This mirror sector is a possible candidate for the dark matter in the universe
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