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Moduli Stabilization in Toroidal Type IIB Orientifolds

Susanne Reffert, Emanuel Scheidegger

TL;DR

The paper tackles all-moduli stabilization in resolved toroidal Type IIB orientifolds within a KKLT-inspired framework, combining flux-induced stabilization of the dilaton and complex structure with non-perturbative stabilization of Kähler moduli on rigid four-cycles. It develops a concrete geometric program based on toric resolutions of abelian orbifolds, global gluing to form a Calabi–Yau, and a careful analysis of divisor topology and orientifold actions to identify which divisors can generate non-perturbative contributions to the superpotential. Key results include a detailed case study of a $T^6/\mathbb{Z}_{6-II}$ model with $h^{1,1}=35$, the enumeration of exceptional divisors, and the demonstration that many divisors have the right topological properties to contribute to $W_{np}$ while accounting for orientifold-induced moduli. The work lays groundwork for a full F-theory uplift and quantitative assessment of non-perturbative effects, providing a tractable setting to test all-moduli stabilization in string compactifications with calculable geometry.

Abstract

We discuss the first step in the moduli stabilization program a la KKLT for a general class of resolved toroidal type IIB orientifolds. In particular, we discuss their geometry, the topology of the divisors relevant for the D3-brane instantons which can contribute to the superpotential, and some non--trivial aspects of the orientifold action.

Moduli Stabilization in Toroidal Type IIB Orientifolds

TL;DR

The paper tackles all-moduli stabilization in resolved toroidal Type IIB orientifolds within a KKLT-inspired framework, combining flux-induced stabilization of the dilaton and complex structure with non-perturbative stabilization of Kähler moduli on rigid four-cycles. It develops a concrete geometric program based on toric resolutions of abelian orbifolds, global gluing to form a Calabi–Yau, and a careful analysis of divisor topology and orientifold actions to identify which divisors can generate non-perturbative contributions to the superpotential. Key results include a detailed case study of a model with , the enumeration of exceptional divisors, and the demonstration that many divisors have the right topological properties to contribute to while accounting for orientifold-induced moduli. The work lays groundwork for a full F-theory uplift and quantitative assessment of non-perturbative effects, providing a tractable setting to test all-moduli stabilization in string compactifications with calculable geometry.

Abstract

We discuss the first step in the moduli stabilization program a la KKLT for a general class of resolved toroidal type IIB orientifolds. In particular, we discuss their geometry, the topology of the divisors relevant for the D3-brane instantons which can contribute to the superpotential, and some non--trivial aspects of the orientifold action.

Paper Structure

This paper contains 8 sections, 16 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Moduli stabilization for resolved toroidal orbifold models
  3. Toroidal Orbifolds
  4. Resolution of Singularities
  5. The global resolution
  6. Topology of the divisors
  7. Orientifold projection
  8. Outlook

Figures (3)

  • Figure 1: Schematic picture of the fixed set configuration of $\mathbb{Z}_{6-II}$ on $SU(2)^2\times SU(3)\times G_2$
  • Figure 2: Toric diagrams of the resolutions of $\mathbb{C}^3/\mathbb{Z}_{6-II}$
  • Figure 3: Toric diagrams of the resolution of the $\mathbb{C}^3/\mathbb{Z}_{6-II}$ fixed point in $T^6/\mathbb{Z}_{6-II}$. We emphasize that the points in the interior of the boundary are identified with the Dynkin diagrams of $A_1$ and $A_2$ obtained from resolving the $\mathbb{C}^2/\mathbb{Z}_2$ and $\mathbb{C}^2/\mathbb{Z}_3$ fixed lines which intersect in this $\mathbb{C}^3/\mathbb{Z}_{6-II}$ fixed point.