Chiral Asymmetry in Four-Dimensional Open-String Vacua

TL;DR

Constructs four-dimensional $N=1$ chiral open-string vacua from the Type IIB $Z$ orbifold, showing that the Chan-Paton group depends on the NS-NS $B$ field and that the maximal group is $SO(8)\times SU(12)\times U(1)$ with three chiral families in $(8,12^*)+(1,66)$. The anomalous $U(1)$ is canceled by a Green-Schwarz mechanism, giving the $U(1)$ gauge boson a string-scale mass and enabling a dual heterotic model with non-standard embedding that reproduces the perturbative spectrum. The paper analyzes low-energy interactions, including a fixed Yukawa coupling and D-term structure with a Fayet-Iliopoulos term, and discusses flat directions, non-perturbative dynamics, and potential IR physics. It also surveys the role of quantized $B$-field backgrounds and modular invariants in generating a variety of open-string descendants, highlighting the implications for chirality and possible phenomenological routes.

Abstract

Starting from the type IIB string on the Z orbifold, we construct some chiral open-string vacua with N=1 supersymmetry in four dimensions. The Chan-Paton group depends on the (quantized) NS-NS antisymmetric tensor. The largest choice, SO(8)xSU(12)xU(1), has an anomalous U(1) factor whose gauge boson acquires a mass of the order of the string scale. The corresponding open-string spectrum comprises only Neumann strings and includes three families of chiral multiplets in the (8,12*) + (1,66) representation. A comparison is drawn with a heterotic vacuum with non-standard embedding, and some properties of the low-energy effective field theory are discussed.