Three-family supersymmetric Pati-Salam models with symplectic groups from intersecting D6-branes

The hidden sector variations in the ${\cal N}=1$ supersymmetric three-family Pati-Salam models with symplectic groups from intersecting D6-branes

“…This seemingly minor change from SU (2) to USp(2) group is quite restrictive and drastically reduces the number of consistent threefamily models. Therefore, while the number of three-family models with SU(4) C × SU(2) L × SU(2) R groups is found to be 202,752 [10,11], the similar models by replacing either one of the SU(2) factors with a USp(2) is only 5 [13]. Interestingly, three-family supersymmetric Pati-Salam model with the specific gauge group SU(4) C × USp(2) L × USp(2) R are even more constrained and we have only found two such models.…”

“…Three-family supersymmetric Pati-Salam with the gauge group U(4) C ×USp(2) L ×SU(2) R have been recently discussed in ref. [13]. It was found that the number of such models is only 5.…”

“…The construction of U Sp(2) groups can be readily achieved by taking the corresponding stacks of D6-branes parallel to any of the O6-planes or their Z 2 images as exemplified in refs. [12,13]. The choice of U Sp( 2) is simpler to deal with since there is no associated global anomalous U (1) group which is generic in the unitary groups.…”

“…[6]. We employ similar conventions to construct supersymmetric Pati-Salam models with symplectic groups [13]. In the orientifold T 6 /(Z 2 × Z 2 ), T 6 is a product of three 2-tori with the orbifold group (Z 2 × Z 2 ) has the generators θ and ω which act on the complex coordinates z i as,…”

“…The effective gauge symmetry of supersymmetric Pati-Salam models can be further broken down to the standard model gauge symmetry via brane splitting. The relevant details and the formulae of computing gauge kinetic functions and the gauge coupling relations are given in [9,12,13].…”