D3/D7 Branes at Singularities: Constraints from Global Embedding and Moduli Stabilisation

TL;DR

This work constructs a fully globally consistent type IIB setup embedding local D3/D7-brane models at dP0 singularities into a compact CY orientifold with moduli stabilisation. Using a LARGE Volume Scenario framework, it achieves a Minkowski (or slightly de Sitter) vacuum with spontaneous SUSY breaking and TeV-scale soft terms, while dynamically aligning the intermediate-scale unification of gauge couplings with the stabilized vacuum parameters. The explicit dP0 left-right model exhibits three chiral families and gauge coupling unification at $M_s\sim10^{12}$ GeV, driven by the global brane content, fluxes, and LVS moduli; however, realistic Yukawa textures may require extending to higher del Pezzo surfaces. Overall, the paper demonstrates the feasibility and constraints of global embeddings with flavour branes and highlights tensions between local model-building flexibility and global consistency, offering a concrete path toward more realistic string-based phenomenology.

Abstract

In the framework of type IIB string compactifications on Calabi-Yau orientifolds we describe how to construct consistent global embeddings of models with fractional D3-branes and connected `flavour' D7-branes at del Pezzo singularities with moduli stabilisation. Our results are applied to build an explicit compact example with a left-right symmetric model at a dP_0 singularity which features three families of chiral matter and gauge coupling unification at the intermediate scale. We show how to stabilise the moduli obtaining a controlled de Sitter minimum and spontaneous supersymmetry breaking. We find an interesting non-trivial dynamical relation between the requirement of TeV-scale soft terms and the correct phenomenological values of the unified gauge coupling and unification scale.

Figures (4)

• Figure 1: The dP$_0$ quiver encoding the $SU(n_0)\times SU(n_1)\times SU(n_2)$ gauge theory with flavour branes. Potential D7-D7 states are not shown.
• Figure 2: The dP$_0$ quiver encoding the $SU(3)\times SU(2)^2$ gauge theory with flavour branes. Again only D3-D3 and D3-D7 states are shown.
• Figure 4: Vacuum energy as a function of $x=\log_{10}{\cal V}$ for different values of $W_0$: $W_0=1\,\text{(blue line)}$, $W_0=10^{-4}\,\text{(yellow line)}$, $W_0=10^{-7}\,\text{(purple line)}$, $W_0=10^{-14}\,\text{(green line)}$;
• Figure 5: Gauge coupling unification in the left-right symmetric model for a unified coupling $\alpha_{\rm unif}^{-1}=19,$ a string scale $M_{s}=9\cdot 10^{11} {\rm GeV},$ and a breaking scale of $SU(2)_R\times U(1)_{\textmd{B-L}}\to U(1)_Y$ at $10\ {\rm TeV}$ after which we assume only one pair of Higgses to be massless. The running of the various couplings is colour-coded as follows: $\alpha_3^{-1}$ (red), $\frac{3}{32} \alpha^{-1}_{\textmd{B-L}}$ (purple), $\alpha^{-1}_{2L,2R}$ (dark-blue), and $\alpha_{Y}^{-1}$ (green). The experimentally observed values of the gauge couplings at $M_Z$ are indicated with the respective disks.