No abstract

Motivated by M-theory/superstring inspired models, we investigate certain behaviors of the deflection angle and the shadow geometrical shapes of higher dimensional quintessential black holes associated with two values of the dark energy (DE) state parameter, being ω = − 1 3 and ω = − 2 3 . Concretely, we derive the geodesic equation of photons on such backgrounds. Thanks to the Gauss–Bonnet theorem corresponding to the optical metric, we compute the leading terms of the deflection angle in the so-called weak-limit approximation. After that, we inspect the effect of DE and the space–time dimension d on the calculated optical quantities. Introducing DE via the field intensity c and the state parameter ω, we find that the shadow size and the deflection angle increase by increasing values of the field intensity c. However, we observe that the high dimensions decrease such quantities for ω-models exhibiting similar behaviors. Then, we consider the effect of the black hole charge, on these optical quantities, by discussing the associated behaviors. The present investigation recovers certain known results appearing in ordinary four dimensional models.

Using instanton effects, we discuss the problem of fermion mass hierarchies in an MSSM-like Type IIA orientifolded model with U(3) × Sp(1) × U(1) × U(1) gauge symmetry obtained from intersecting D6-branes. In the corresponding four-stack quiver, the different scales of the generated superpotential couplings offer a partial solution to fermion mass hierarchies. Using the known data with neutrino masses τ < ∼ 2 eV, we give the magnitudes of the relevant scales.

In the context of type-IIA orientifold compactifications, we discuss the fermion masses in a two-singlet-extended minimal-supersymmetric-standard-model four-stack quiver with 𝑈 (3) × 𝑆𝑝(1) × 𝑈 (1) × 𝑈 (1) gauge symmetry. The corresponding effective superpotential exhibits hierarchical coupling term scales giving a partial solution to the fermion masses problem. Using the known data with upper bound neutrino masses 𝑚𝜈 𝜏 2 eV, we estimate the relevant scales for the model.

We discuss the fermion masses in a string-inspired scalar extension of the standard model in four stacks of intersecting D-branes with a flavor-dependent symmetry. A complex scalar field S is required to generate all fermion Yukawa couplings. The latter are successively suppressed and their magnitudes weight the scales of fermion masses and offer a partial solution to the hierarchy problem. Using the known data, we estimate the relevant scales for the model.