Revisiting the supersymmetric Pati–Salam models from intersecting D6-branes

Abstract

Employing novel random and supervised scanning methods, we systematically revisit the construction of three-family $$N=1$$ N = 1 supersymmetric Pati–Salam models in Type IIA orientifolds on $$\mathbf{T}^6/({\mathbb {Z}}_2\times {\mathbb {Z}}_2)$$ T 6 / ( Z 2 × Z 2 ) with intersecting D6-branes. Arising from the stacks of D6-branes with U(n) gauge symmetries, the Pati–Salam gauge symmetries $$SU(4)_C\times SU(2)_L \times SU(2)_R$$ S U ( 4 ) C × S U ( 2 ) L × S U ( 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 $${{\mathbb {Z}}_2}$$ 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 $$SU(2)_L$$ S U ( 2 ) L and $$SU(2)_R$$ S U ( 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.

Four-Family ${\cal N}=1$ Supersymmetric Pati-Salam Models from Intersecting D6-Branes

“…The sixth class of models are with large wrapping numbers 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, represented by Models 26-35 which did not appear in the former search. Three-family models with large wrapping number 5 have been found in [51], but it's the first time to find four-family models with wrapping numbers at this scale.…”

“…Due to the supersymmetry breaking and moduli stabilization triggered by their two confining groups in the hidden sectors, these models do have realistic and phenomenological consequences, as shown in Refs. [43,51,52]. Until very recent, intriguingly all possible 202752 three-family N = 1 supersymmetric Pati-Salam models on Ì 6 / 2 × 2 have been found and classified with 33 type of independent models according to gauge coupling relations [1].…”

The Supersymmetry Breaking Soft Terms, and Fermion Masses and Mixings in the Supersymmetric Pati-Salam Model from Intersecting D6-branes

“…For concreteness, we choose Model 16 from Ref. [6], which is T-dual to Model 18, see Table 3. The model exhibits approximate gauge coupling unification with three-generations of chiral fermions together besides the hidden sector with gauge group U Sp(2) 2 .…”

“…Recently in Ref. [6] some new supersymmetric Pati-Salam models from intersecting D6-branes on a T 6 /(Z 2 × Z 2 ) orientifold in IIA string theory have been constructed using the methods of machine learning. Here, we discuss the phenomenology of a particular class of these newly found models where one of the wrapping numbers is 5.…”

The Complete Search for the Supersymmetric Pati-Salam Models from Intersecting D6-Branes

“…In [36,37], we constructed supersymmetric Pati-Salam models and generalized Pati-Salam mod-els on Type IIA T 6 /(Z 2 × Z 2 ) orientifolds with D6-branes intersecting at generic angles to obtain the massless open string state spectra. In particular, in [36], we systematically studied the threefamily N = 1 supersymmetric Pati-Salam model building in Type IIA orientifolds on T 6 /(Z 2 × Z 2 ) with intersecting D6-branes in which the SU(4) C × SU(2) L × SU(2) R gauge symmetries arise from U(n) branes. We also found that the Type II T-duality in the previous study [11] is not an equivalence relation in Pati-Salam model building as most of the models are not invariant under SU(2) L and SU(2) R exchange.…”