GUTs in Type IIB Orientifold Compactifications

TL;DR

This work develops a framework for globally consistent SU(5) GUT constructions in Type IIB orientifolds with O3/O7 planes, placing D7-branes on rigid del Pezzo surfaces and breaking GUT symmetry via U(1)_Y flux. It derives comprehensive global consistency conditions (tadpoles, K-theory, Freed-Witten quantization, D-/F-term constraints) and demonstrates explicit globally consistent models, including a three-generation example with all matter localized on curves and a D3-instanton-generated top Yukawa coupling. By exploring del Pezzo transitions of both the elliptic fibration over del Pezzo bases and the Quintic, the paper exposes a rich landscape of geometries (including swiss-cheese and non-swiss-cheese phases) suitable for GUT model building and potential LARGE volume moduli stabilization. The results indicate that these orientifold constructions can capture many salient GUT features and motivate further study of their F-theory uplifts and global moduli-stabilization dynamics, with implications for phenomenology and collider signatures.

Abstract

We systematically analyse globally consistent SU(5) GUT models on intersecting D7-branes in genuine Calabi-Yau orientifolds with O3- and O7-planes. Beyond the well-known tadpole and K-theory cancellation conditions there exist a number of additional subtle but quite restrictive constraints. For the realisation of SU(5) GUTs with gauge symmetry breaking via U(1)_Y flux we present two classes of suitable Calabi-Yau manifolds defined via del Pezzo transitions of the elliptically fibred hypersurface P_{1,1,1,6,9}[18] and of the Quintic P_{1,1,1,1,1}[5], respectively. To define an orientifold projection we classify all involutions on del Pezzo surfaces. We work out the model building prospects of these geometries and present five globally consistent string GUT models in detail, including a 3-generation SU(5) model with no exotics whatsoever. We also realise other phenomenological features such as the 10 10 5 Yukawa coupling and comment on the possibility of moduli stabilisation, where we find an entire new set of so-called swiss-cheese type Calabi-Yau manifolds. It is expected that both the general constrained structure and the concrete models lift to F-theory vacua on compact Calabi-Yau fourfolds.

Figures (9)

• Figure 1: The five different triangulations of the toric ${\rm dP}_2$ base.
• Figure 2: The points of the polyhedron of the ${\rm dP}_3$ base.
• Figure 3: Schematics of the intersecting del Pezzo surfaces on transitions of the quintic. Each intersection is a $\mathbb{P}^1$.
• Figure 4: Symmetry of the toric polytope defining $\mathbb{P}^2$.
• Figure 5: The toric polytope defining $\mathbb{P}^1\times \mathbb{P}^1$.

Theorems & Definitions (1)

• Theorem 1: Manin