Blowing-Up the Four-Dimensional Z_3 Orientifold

TL;DR

This work investigates the blowing-up of the four-dimensional $N=1$ ABPSS $Z_3$ orientifold by giving VEVs to twisted-sector moduli, which induces a Fayet–Iliopoulos term for an anomalous $U(1)$. The authors derive the explicit FI term, analyze anomaly cancellation via Green–Schwarz couplings, and perform a detailed restabilization of the vacuum when non-Abelian fields must acquire VEVs to preserve SUSY. They construct $D$- and $F$-flat directions using holomorphic gauge-invariant polynomials, focusing on $\chi^6$ monomials, and show that the restabilized vacuum generically breaks the gauge group to $SU(2)^6\times SO(8)$ with only one light family, though special alignments can enhance symmetry to $Sp(2k)$. The results illustrate the concrete link between blowing-up moduli, FI terms, and gauge-spectrum reshaping in Type I orientifolds, providing a framework that can be extended to other blown-up models despite the specific ABPSS case not being phenomenologically viable.

Abstract

We study the blowing-up of the four-dimensional Z_3 orientifold of Angelantonj, Bianchi, Pradisi, Sagnotti and Stanev (ABPSS) by giving nonzero vacuum expectation values (VEV's) to the twisted sector moduli blowing-up modes. The blowing-up procedure induces a Fayet-Iliopoulos (FI) term for the ``anomalous'' U(1), whose magnitude depends linearly on the VEV's of the blowing-up modes. To preserve the N=1 supersymmetry, non-Abelian matter fields are forced to acquire nonzero VEV's, thus breaking (some of) the non-Abelian gauge structure and decoupling some of the matter fields. We determine the form of the FI term, construct explicit examples of (non-Abelian) D and F flat directions, and determine the surviving gauge groups of the restabilized vacua. We also determine the mass spectra, for which the restabilization reduces the number of families.