D-Branes at del Pezzo Singularities: Global Embedding and Moduli Stabilisation

TL;DR

This work demonstrates a concrete route to fully global Type IIB string compactifications where D-branes at del Pezzo singularities realize a visible sector while all Kähler moduli are stabilised. By classifying Calabi-Yau threefolds with two orientifold-exchanged del Pezzo singularities and embedding the local quiver without flavour branes into a Swiss-cheese geometry, the authors implement both LVS and KKLT-type moduli stabilisation with D-term uplifting to de Sitter vacua. They perform thorough global consistency checks (tadpoles, K-theory, Freed-Witten anomalies) and present a detailed dP0 trinification model illustrating a path to the Standard Model within this framework. The paper also discusses higher del Pezzo cases without flavour branes and lays out open questions, including extending to h11≥6, incorporating flavour branes and F-theory, and connecting to cosmology and particle phenomenology.

Abstract

In the context of type IIB string theory we combine moduli stabilisation and model building on branes at del Pezzo singularities in a fully consistent global compactification. By means of toric geometry, we classify all the CY manifolds with 3 < h11 < 6 which admit two identical del Pezzo singularities mapped into each other under the orientifold involution. This effective singularity hosts the visible sector containing the Standard Model while the Kaehler moduli are stabilised via a combination of D-terms, perturbative and non-perturbative effects supported on hidden sectors. We present concrete models where the visible sector, containing the Standard Model, gauge and matter content, is built via fractional D3-branes at del Pezzo singularities and all the Kaehler moduli are fixed providing an explicit realisation of both KKLT and LARGE volume scenarios, the latter with D-term uplifting to de Sitter minima. We perform the consistency checks for global embedding such as tadpole, K-theory charges and Freed-Witten anomaly cancellation. We briefly discuss phenomenological and cosmological implications of our models.

Figures (6)

• Figure 1: A Swiss cheese type CY manifold with four Kähler moduli ($h^{1,1}=4$ and $h^{1,1}_-=1$). The CY contains two dP$_0$ 4-cycles that are exchanged under an orientifold involution. On top of the O7-planes on the remaining two four-cycles, D7-branes are wrapped that lead to gaugino condensation needed for moduli stabilisation.
• Figure 2: Left: The dP$_0$ quiver encoding the well-known $SU(n)^3$ gauge theory (in the absence of flavour branes) and three bi-fundamental fields between the different $SU(n)$ factors. Right: The specific case of $n=3$ which gives rise to the trinification model based on three copies of $SU(3)$. The labels $SU(3)_C\times SU(3)_L\times SU(3)_R$ indicate which of the $SU(3)$ factors gives rise to which SM gauge groups.
• Figure 3: Minkowski vacuum at ${\cal V}= 4\cdot 10^6$ for natural values of the underlying parameters $W_0\simeq 0.2$ and $g_s\simeq 0.03$.
• Figure 4: Left: The general $dP_1$ quiver with unequal ranks, no flavour branes and anomaly cancellation. Right: A phenomenologically interesting case of the general quiver on the left with $n=j=1.$
• Figure 5: Left: The general $dP_2$ quiver with unequal ranks, no flavour branes and anomaly cancellation. Right: The quiver of $dP_3$ with unequal ranks, no flavour branes and anomaly cancellation.