Realistic D-Brane Models on Warped Throats: Fluxes, Hierarchies and Moduli Stabilization

TL;DR

This work builds explicit string-theoretic realizations of the Randall–Sundrum idea by embedding D-branes at singularities inside highly warped KS-like throats in flux compactifications. The authors integrate a bottom-up D-brane approach with flux-induced warping, yielding semirealistic spectra (including Standard Model and Left–Right variants) localized at the throat tip, and stabilise much of the moduli via $3$-form fluxes (dilaton and complex structure) and D-term/nonperturbative effects for the Kähler moduli. They present two main scenarios—Standard Model on anti-D3-branes or on D3-branes—along with explicit Pati–Salam and LR constructions, and analyze related phenomenology such as gauge coupling unification, hypercharge embedding, proton stability, Yukawa couplings, and possible soft terms induced by fluxes. The framework points toward fully stabilised, potentially de Sitter vacua, with rich phenomenological implications and several avenues for further, more detailed model-building and holographic interpretation.

Abstract

We describe the construction of string theory models with semirealistic spectrum in a sector of (anti) D3-branes located at an orbifold singularity at the bottom of a highly warped throat geometry, which is a generalisation of the Klebanov-Strassler deformed conifold. These models realise the Randall-Sundrum proposal to naturally generate the Planck/electroweak hierarchy in a concrete string theory embedding, and yielding interesting chiral open string spectra. We describe examples with Standard Model gauge group (or left-right symmetric extensions) and three families of SM fermions, with correct quantum numbers including hypercharge. The dilaton and complex structure moduli of the geometry are stabilised by the 3-form fluxes required to build the throat. We describe diverse issues concerning the stabilisation of geometric Kahler moduli, like blow-up modes of the orbifold singularities, via D term potentials and gauge theory non-perturbative effects, like gaugino condensation. This local geometry, once embedded in a full compactification, could give rise to models with all moduli stabilised, and with the potential to lead to de Sitter vacua. Issues of gauge unification, proton stability, supersymmetry breaking and Yukawa couplings are also discussed.

Figures (13)

• Figure 1: Description of a deformed conifold with 3-form fluxes (a KS throat) embedded in a compact geometry, with anti-D3-branes trapped at the tip of the throat. Beyond the throat, the compactifications may include other ingredients, like D7-branes wrapped on 4-cycles, etc, which are not relevant for the generation of the warp factor on the throat, but may lead to other interesting effects (like non-perturbative superpotentials).
• Figure 2: An illustration of the bottom-up approach. D3-branes at an orbifold singularity provide examples of chiral theories in which the Standard Model can be embedded. Most of the properties of the model depend on the structure of the singularity. This local model can then be embedded in many different string compactifications, as long as the compact manifold has the same type of orbifold singularity.
• Figure 3: This is the quiver diagram corresponding to a general $\bf C^3 /\bf Z_3$ model. In the non-SUSY case (models with $\overline{\textrm{D3}}$ and D7-branes), fermions and scalars transform in different representations of the gauge group, namely those displayed (respectively) in a) and b).For the supersymmetric case, both scalars and fermions fill in chiral multiplets of the preserved SUSY, and transform in the bifundamentals displayed in c).
• Figure 4: Description of the conifold geometry as a double $\bf C^*$ fibration.
• Figure 5: Simplified pictorial depiction of the conifold and its $\bf S^3$. The dot and the cross denote the degeneration points of the two $\bf C^*$ fibrations, respectively.