Erratum to: “Towards the supersymmetric standard model from intersecting D6-branes on the Z6′ orientifold” [Nucl. Phys. B 755 (2006) 79]

Abstract

We construct N = 1 supersymmetric fractional branes on the Z ′ 6 orientifold. Intersecting stacks of such branes are needed to build a supersymmetric standard model. If a, b are the stacks that generate the SU (3) c and SU (2) L gauge particles, then, in order to obtain just the chiral spectrum of the (supersymmetric) standard model (with non-zero Yukawa couplings to the Higgs mutiplets), it is necessary that the number of intersections a • b of the stacks a and b, and the number of intersections a • b ′ of a with the orientifold image b ′ of b satisfy (a • b, a • b ′ ) = ±(2, 1) or ±(1, 2). It is also necessary that there is no matter in symmetric representations of the gauge group, and not too much matter in antisymmetric representations, on either stack. We provide a number of examples having these properties. Different lattices give different solutions and different physics.

Towards the field theory of the Standard Model on fractional D6‐branes on T6/ℤ6′: Yukawa couplings and masses

“…For interaction terms such as Yukawa couplings, exact string theoretic results are only known on the six-torus, e.g. [8,9], and its T 6 /Z 2 × Z 2 orbifold without discrete torsion, and consequently a treatment of Standard Model (SM) vacua in globally consistent supersymmetric D6-brane models on T 6 /Z 6 [10,11,12,13,3,7] or other T 6 /Z 2N [14,15,16] and T 6 /Z 2 × Z 2M backgrounds with discrete torsion [17,18] has not been performed. To go one step further in the understanding of the field theory of intersecting fractional D6-brane SM vacua, we assume here that the formula for Yukawa couplings on the six-torus directly carries over to its orbifolds and extends to the new case with chiral matter at one vanishing angle, i.e.…”

Orientifold's landscape: non-factorisable six-tori

“…More concretely, intersecting D-brane models in toroidal orientifold compactifications, represent a simple yet rich set-up. Particle physics models, with spectra close to that of the Standard Model, both in non-supersymmetric [6][7][8][9][10][11][12][13][14][15][16] as well as supersymmetric [17][18][19][20][21][22][23][24][25][26] configurations, can be constructed (for reviews and more references see [27]).…”

The supersymmetric standard model from the Z[sub 6][sup ʹ] orientifold?

“…We have shown [11] that, unlike the Z 6 orientifold, at least on some lattices, the Z 6 orientifold can support supersymmetric stacks a and b of D6-branes with intersection numbers satisfying (a • b, a • b ) = (2, 1) or (1, 2). Stacks having this property are an indispensable ingredient in any intersecting brane model that has just the matter content of the (supersymmetric) standard model.…”

“…Here we address this question for the Z ′ 6 orientifold. Further details of this work may be found in reference [11].…”