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Rigour and rigidity: Systematics on particle physics D6-brane models on \(\mathbb{Z}_{2} \times \mathbb{Z}_{6}\). (English) Zbl 1338.81396

Summary: We launch a systematic search for phenomenologically appealing string vacua with intersecting D-branes on the promising \(T^{6}/(\mathbb{Z}_{2} \times \mathbb{Z}_{6} \times \Omega \mathcal{R})\) orientifold with discrete torsion. The number of independent background lattices is reduced from six to two by new symmetries. The occurrence of \(\operatorname{USp}(2N)\) and \(\operatorname{SO}(2N)\) versus \(\operatorname{U}(N)\) gauge groups is classified as well as D-branes without matter in the adjoint and/or symmetric representation. Supersymmetric fractional D6-branes allowing for RR tadpole cancellation are fully classified in terms of all possible values of the one complex structure modulus inherited from the underlying six-torus. We then systematically investigate the conditions for three particle generations at pairwise intersections of two D6-branes.
Global \(\operatorname{SU}(5)\) GUT models on \(T^{6}/(\mathbb{Z}_{2} \times \mathbb{Z}_{6} \times \Omega \mathcal{R})\) are excluded by demanding three generations and no exotic matter in the 15 representation. Two prototypes of global Pati-Salam models with a mild amount of vector-like exotic matter are found.

MSC:

81V22 Unified quantum theories
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
83E30 String and superstring theories in gravitational theory
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
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