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Coset space dimensional reduction and Wilson flux breaking of ten-dimensional \(\mathcal{N}=1\), \(E_8\) gauge theory. (English) Zbl 1189.81144

Summary: We consider a \(\mathcal{N}=1\) supersymmetric \(E _{8}\) gauge theory, defined in ten dimensions and we determine all four-dimensional gauge theories resulting from the generalized dimensional reduction à la Forgacs-Manton over coset spaces, followed by a subsequent application of the Wilson flux spontaneous symmetry-breaking mechanism. Our investigation is constrained only by the requirements that (i) the dimensional reduction leads to the potentially phenomenologically interesting, anomaly-free, four-dimensional \(E _{6}\), \(SO_{10}\) and \(SU_{5}\) GUTs and (ii) the Wilson flux mechanism makes use only of the freely acting discrete symmetries of all possible six-dimensional coset spaces.

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
81T17 Renormalization group methods applied to problems in quantum field theory
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