Chiral Supersymmetric Standard Model Spectra from Orientifolds of Gepner Models

TL;DR

The paper addresses constructing four-dimensional $N=1$ orientifold vacua with the chiral Standard Model content from Gepner-model based CFTs by scanning all simple-current invariants of $c=9$ tensor products of $N=2$ minimal models. It develops a framework using boundary and crosscap states, simple-current modular invariants, and tadpole cancellation to realize SM-like spectra on four-stack brane configurations, finding multiple viable tensor combinations and orientifolds. The results show a large number of consistent spectra, often with an $Sp(2)$ weak sector and abundant non-chiral exotics, with some models achieving massless hypercharge and varying $B-L$ masses; in a few cases thousands of distinct open-string solutions exist for a given tensor product. The study demonstrates that non-toric RCFT orientifolds can yield numerous SM-like chiral vacua, highlighting both the richness of the landscape and the need for additional constraints to isolate phenomenologically attractive models.

Abstract

We construct d=4,N=1 orientifolds of Gepner models with just the chiral spectrum of the standard model. We consider all simple current modular invariants of c=9 tensor products of N=2 minimal models. For some very specific tensor combinations, and very specific modular invariants and orientifold projections, we find a large number of such spectra. We allow for standard model singlet (dark) matter and non-chiral exotics. The Chan-Paton gauge group is either U(3) x Sp(2) x U(1) x U(1) or U(3) x U(2) x U(1) x U(1). In many cases the standard model hypercharge U(1) has no coupling to RR 2-forms and hence remains massless; in some of those models the B-L gauge boson does acquire a mass.