Three Family Type IIB Orientifold String Vacua with Non-Abelian Wilson Lines

TL;DR

The paper advances the construction of perturbative ${D}=4$, ${N}=1$ Type IIB orientifolds with non-Abelian Wilson lines to realize a three-family spectrum. It develops an explicit $Z_3\times Z_2\times Z_2$ orientifold with a single Wilson line, yielding a gauge group $$(U(4)\times U(2)\times SU(2)\times SU(2))^2\times (U(6)\times Sp(4))^2$$ and a detailed massless spectrum with a trilinear superpotential. Abelian gauge anomalies are shown to cancel via a generalized Green-Schwarz mechanism involving twisted RR moduli, with subtle non-Abelian Wilson-line effects; Fayet-Iliopoulos terms and gauge-coupling corrections from blowing-up moduli are computed and organized by brane sector. The results provide a concrete, anomaly-free framework near Standard-Model-like structure and establish a blueprint for extending these constructions to other orbifolds and non-Abelian Wilson lines while exploring phenomenological implications.

Abstract

We address the implementation of non-Abelian Wilson lines in D=4 N=1 Type IIB orientifold constructions. We present an explicit three-family example with the gauge group (U(4)xU(2)xSU(2)xSU(2))^2x(U(6)xSp(4))^2 and give the particle spectrum and the trilinear superpotential. Emphasizing the new subtleties associated with the introduction of non-Abelian Wilson lines, we show that the Abelian gauge anomalies are cancelled by the Green-Schwarz-type mechanism, and calculate the Fayet-Iliopoulos terms and gauge coupling corrections. The analysis thus sets a stage for further investigations of the phenomenological implications of this model.