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Schoen manifold with line bundles as resolved magnetized orbifolds. (English) Zbl 1342.81462
Summary: We give an alternative description of the Schoen manifold as the blow-up of a \(2\times 2\) orbifold in which one 2-factor acts as a roto-translation. Since for this orbifold the fixed tori are only identified in pairs but not orbifolded, four-dimensional chirality can never be obtained in heterotic string compactifications using standard techniques alone. However, chirality is recovered when its tori become magnetized. To exemplify this, we construct an \(E_8\times E_8'\) heterotic \(\mathrm{SU}(5)\) GUT on the Schoen manifold with Abelian gauge fluxes, which becomes an MSSM with three generations after an appropriate Wilson line is associated to its freely acting involution. We reproduce this model as a standard heterotic orbifold CFT of the (partially) blown down Schoen manifold with a magnetic flux. Finally, in analogy to a proposal for non-perturbative heterotic models by G. Aldazabal et al. [Nucl. Phys., B 519, No. 1–2, 239–281 (1998; Zbl 0945.81050)] we suggest modifications to the heterotic orbifold spectrum formulae in the presence of magnetized tori.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory
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