Local String Models and Moduli Stabilisation

TL;DR

This paper reviews local string models with a focus on moduli stabilisation, SUSY breaking, and global embedding within Calabi–Yau compactifications, highlighting Type IIB D-brane constructions and the Large Volume Scenario (LVS). It explains how fluxes generate a landscape of vacua via $W_0(S,U)$ and non-perturbative effects $W_{np}= abla\sum_i A_i e^{-a_i T_i}$, producing KKLT-like SUSY AdS minima or LVS AdS minima at large volume with a characteristic hierarchy $M_s$, $M_{KK}$, $m_{3/2}$, $m_V$, and requires $|W_0|\\ll V^{1/3}$ for EFT control. SUSY breaking in LVS is driven by the Kähler moduli F-terms, with the SM cycle commonly fixed by D-terms due to BMP constraints, leading to sequestered or non-sequestered soft terms and a cosmological moduli problem in many scenarios. The article demonstrates fully explicit global embeddings of local, chiral models (e.g., using $dP_n$ singularities) in LVS compactifications that can yield de Sitter vacua with computable soft terms, including a left-right symmetric example with intermediate-scale unification; it also outlines open questions about inflation, cosmology, higher-order corrections, and observable tests such as dark radiation or cosmic axion backgrounds to connect to data.

Abstract

A brief overview is presented of the progress made during the past few years on the general structure of local models of particle physics from string theory including: moduli stabilisation, supersymmetry breaking, global embedding in compact Calabi-Yau compactifications and potential cosmological implications. Type IIB D-brane constructions and the Large Volume Scenario (LVS) are discussed in some detail emphasising the recent achievements and the main open questions.

Figures (3)

• Figure 1: The simplest realisation of a chiral model at D3 brane singularities containing the SM (the trinification model at $dP_0$ in this case). The three gauge groups are identical, $SU(3)^3$. The three arrows imply three families of bi-fundamental fields. The equal number of ingoing and outgoing arrows at each node guarantees anomaly cancellation.
• Figure 2: An explicit global embedding of local D-brane models. The SM is located at a $dP_0$ mapped to an identical singularity by a $\mathbb{Z}_2$ twist. Two ther 4-cycles are needed to stabilise Kähler moduli and obtain a global realisation of LVS with chiral matter.
• Figure 4: Unification in Left-Right symmetric model with low energy RG running matching the unification scale and gauge coupling with those values obtained independently from moduli stabilisation.