Abstract
Employing novel random and supervised scanning methods, we systematically revisit the construction of three-family N=1 supersymmetric Pati–Salam models in Type IIA orientifolds on mathbf{T}^6/({mathbb {Z}}_2times {mathbb {Z}}_2) with intersecting D6-branes. Arising from the stacks of D6-branes with U(n) gauge symmetries, the Pati–Salam gauge symmetries SU(4)_Ctimes SU(2)_L times SU(2)_R can be broken down to the Standard Model via D-brane splitting as well as D- and F-flatness preserving Higgs mechanism. Also, the hidden sector contains USp(n) branes, which are parallel with the orientifold planes or their {{mathbb {Z}}_2} images. We find that the Type II T-duality in the previous study is not an equivalent relation in Pati–Salam model building if the model is not invariant under SU(2)_L and SU(2)_R exchange, and provides a way to obtain new models. We systematically construct the new models with three families, which usually do not have gauge coupling unification at the string scale. We for the first time construct the Pati–Salam models with at least one wrapping number whose absolute value reaching 5. In particular, for one large wrapping number equal to 5, we find that one kind of model carries more refined gauge couplings, and thus with more possibilities to have approximate gauge coupling unification.
Highlights
The goal of string phenomenology is to construct the N = 1 supersymmetric Standard Models (SM) or the SM from string theories
Let us briefly review the basic rules to construct the supersymmetric models on Type IIA T 6/(Z2 × Z2) orientifolds with D6-branes intersecting at generic angles, as well as to obtain the massless open string state spectra in Refs
With dimension reduction method “AutoEncoder”, we observe in Fig. 2 that according to the wrapping numbers of D6-brane models: each point corresponds to a D6brane model, and the Minimal Supersymmetric SM (MSSM)-like models are highlighted with green points when the wrapping number is less than 5, Fig. 1 AutoEncoder dimension reduction
Summary
Within the intersecting D6-brane models on Type IIA orientifolds [14,15,16], many non-supersymmetric three-family Standard-like models and grand unified models have been constructed [14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35] They typically suffer from the large Planck scale corrections at the loop level, or in other words, there exists the gauge hierarchy problem.
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