GUTs in Type IIB Orientifold Compactifications

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.

• The paper presents globally consistent SU(5) GUT models constructed with intersecting D7-branes that satisfy crucial string theory constraints like tadpole and K-theory charge cancellation.
• It introduces detailed methodologies for building Calabi-Yau threefolds with del Pezzo surfaces, employing elliptic fibrations and del Pezzo transitions to meet global consistency.
• Practical model examples demonstrate how U(1)_Y flux breaks GUT symmetry and how D3-brane instantons induce Yukawa couplings, supporting a realistic particle physics spectrum.

Overview of Global Consistent $SU(5)$ GUT Models in Type IIB Orientifold Compactifications

The paper presents a detailed examination of globally consistent $SU(5)$ Grand Unified Theories (GUTs) realized within Type IIB orientifold compactifications on Calabi-Yau threefolds with intersecting D7-branes. This analysis is driven by the necessity to satisfy stringent consistency conditions integral to string theory, such as tadpole cancellation and K-theory charge cancellation, in order to develop viable models that extend the Standard Model of particle physics.

Framework and Constraints

The authors systematically analyze $SU(5)$ GUT models focusing on intersecting D7-branes on genuine Calabi-Yau orientifolds. The orientifolded models must incorporate O3- and O7-planes, respecting the sophisticated constraints of tadpole and K-theory cancellation. Distinctively, the approach involves examining globally consistent configurations needed when employing both GUT breaking via $U(1)_Y$ flux and inherent stringy constructions.

The paper emphasizes the complexity of formulating these models, underpinned by configurations such as the tadpole cancellation conditions and constraints on gauge bundles due to the Freed-Witten anomaly. These constraints highlight the quantization of gauge flux on D7-branes wrapping rigid del Pezzo surfaces, which often are not Spin manifolds, calling for careful flux quantization.

Construction of Calabi-Yau Threefolds

The study targets Calabi-Yau threefolds with del Pezzo base surfaces, derived through two technical methodologies: elliptic fibration over del Pezzo surfaces and del Pezzo transitions. These geometric configurations facilitate the establishment of GUT models with appropriate brane setups while ensuring susceptibility to global consistency checks. The classification of involutions on del Pezzo surfaces plays a crucial role, providing a foundational understanding essential for constructing these Calabi-Yau manifolds with the desired properties.

Model Building and GUT Phenomenology

In their quest to illustrate the practical application of this framework, the authors construct several examples of $SU(5)$ GUT models. Each example serves to demonstrate the feasibility of constructing models that satisfy essential phenomenological properties, such as three-generational matter and GUT symmetry breaking via $U(1)_Y$ flux without introducing vector-like exotics. An important outcome of these investigations is the understanding of how D3-brane instantons can induce otherwise forbidden Yukawa couplings, highlighting the critical interplay between instanton effects and phenomenology.

The models illustrated include configurations with different involutions that optimize the interplay between the model’s phenomenological properties and the geometric structure. The paper details specific geometric setups and line bundle embeddings that realize desired properties, such as reducing additional vector-like matter often arising in these constructions.

Implications and Prospects

The paper concludes by discussing the implications of the constructed models for both string-theoretical model-building and phenomenological applications. Notably, the models serve as a fertile ground for establishing connections between string theory and GUTs, enhancing understanding of consistent string embeddings of realistic physics models.

Future directions pointed out by the authors involve detailed statistical analyses of these classes of models and extending the search to other Calabi-Yau constructions. Also, by aligning these constructions with broader concepts such as moduli stabilization and the LARGE volume scenario, there is potential for linking these models with cosmological observations, offering a comprehensive landscape for future research in string phenomenology and its intersection with particle physics.