Supersymmetric Three Family SU(5) Grand Unified Models from Type IIA Orientifolds with Intersecting D6-Branes

TL;DR

This work investigates constructing ${ m N}=1$ supersymmetric three-family ${ m SU}(5)$ GUTs from Type IIA orientifolds with intersecting D6-branes on $T^6/({f Z}_2 imes{f Z}_2)$. Through a systematic classification of supersymmetric brane configurations and tadpole constraints, the authors show that three-family models with only ${f 10}$-plets are absent unless ${f 15}$-plets are present. They perform a comprehensive cataloging of viable Type III and Type IV brane setups, finding 10 two-stack solutions and 149 three-stack solutions (plus one Type IV continuation), with spectra detailed in the Appendix. While not fully realistic, the results establish a framework for building GUT models in intersecting-brane setups and highlight phenomenological challenges and potential M-theory G2 realizations. The study also points to future explorations of more general orbifolds and symmetry-breaking mechanisms, including Wilson-line–driven GUT breaking.

Abstract

We construct some N=1 supersymmetric three-family SU(5) Grand Unified Models from type IIA orientifolds on $\IT^6/(\IZ_2\times \IZ_2)$ with D6-branes intersecting at general angles. These constructions are supersymmetric only for special choices of untwisted moduli. We show that within the above class of constructions there are no supersymmetric three-family models with 3 copies of {\bf 10}-plets unless there are simultaneously some {\bf 15}-plets. We systematically analyze the construction of such models and their spectra. The M-theory lifts of these brane constructions become purely geometrical backgrounds: they are singular $G_2$ manifolds where the Grand Unified gauge symmetries and three families of chiral fermions are localized at codimension 4 and codimension 7 singularities respectively. We also study somepreliminary phenomenological features of the models.

Figures (4)

• Figure 1: O6-planes in the orientifold of $\bf T^6/(\bf Z_2\times \bf Z_2)$.
• Figure 2: The D6-branes wrap one-cycles on each two-torus. The one-cycles make an angle $\theta$ with the $\Omega R$ orientifold plane which lies along the $R_1$-axis on all three two-tori. The tori can be rectangular (a) or tilted (b).
• Figure 3: The cycle $[a]+\frac{1}{2}[b]$, depicted as cycle C, is not closed for an untilted torus (i). However, for a tilted torus (ii) the complex structure makes C a closed cycle $[a']$.
• Figure 4: O6-planes in the orientifold of $\bf T^6/(\bf Z_2\times \bf Z_2)$ where the third two-tori is tilted.