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Split symmetries. (English) Zbl 1364.83058
Summary: We consider six-dimensional supergravity with gauge group \(\mathrm{SO}(10) \times \mathrm U(1)_A\), compactified on the orbifold \(T^2 / \mathbb{Z}_2\). Three quark-lepton generations arise as zero modes of a bulk 16-plet due to magnetic flux of the anomalous \(\mathrm U(1)_A\). Boundary conditions at the four fixed points break \(\mathrm{SO}(10)\) to subgroups whose intersection is the Standard Model gauge group. The gauge and Higgs sector consist of “split” \(\mathrm{SO}(10)\) multiplets. As a consequence of the \(\mathrm U(1)_A\) flux, squarks and sleptons are much heavier than gauge bosons, Higgs bosons, gauginos and higgsinos. We thus obtain a picture similar to “split supersymmetry”. The flavor structure of the quark and lepton mass matrices is determined by the symmetry breaking at the orbifold fixed points.

MSC:
83E50 Supergravity
81T13 Yang-Mills and other gauge theories in quantum field theory
81V22 Unified quantum theories
81T60 Supersymmetric field theories in quantum mechanics
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