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Yukawa couplings and masses of non-chiral states for the standard model on D6-branes on \(T^6/\mathbb Z_6'\). (English) Zbl 1348.81371
Summary: The perturbative leading order open string three-point couplings for the Standard Model with hidden \(\mathrm{USp}(6)\) on fractional D6-branes on \(T^6\mathbb Z_6'\) from [F. Gmeiner and the first author, “Millions of standard models on \(\mathbb Z'_6\)?”, ibid. 2008, No. 7, Paper No. 052, 49 p. (2008; doi:10.1088/1126-6708/2008/07/052); Nucl. Phys., B 829, No. 1–2, 225–297 (2010; Zbl 1203.81194)] are computed. Physical Yukawa couplings consisting of holomorphic Wilsonian superpotential terms times a non-holomorphic prefactor involving the corresponding classical open string Kähler metrics are given, and mass terms for all non-chiral matter states are derived. The lepton Yukawa interactions are at leading order flavour diagonal, while the quark sector displays a more intricate pattern of mixings. While \(\mathcal N=2\) supersymmetric sectors acquire masses via only two D6-brane displacements – which also provide the hierarchies between up- and down-type Yukawas within one quark or lepton generation – the remaining vector like states receive masses via perturbative three-point couplings to some Standard Model singlet fields with vevs along at directions.
Couplings to the hidden sector and messengers for supersymmetry breaking are briefly discussed.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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