Comments on Gepner Models and Type I Vacua in String Theory

TL;DR

The paper constructs open descendants of Gepner-model vacua to realize Type I string compactifications, concentrating on six-dimensional $N=(1,0)$ theories with varied numbers of tensor multiplets and including cases with no tensors. It develops a systematic framework using $N=2$ spectral flow, modular-invariant SUSY torus amplitudes, fixed-point resolution, and Klein-bottle/Crosscap constraints to generate consistent open sectors and analyze tadpole cancellation. It then provides explicit spectra for three families—$(k=2)^4$ with $Z_2$, $(k=2)^4$ with $Z_4$, and $(k=1)^6$—highlighting anomaly cancellation via a generalized Green–Schwarz mechanism and revealing CP-gauge-group structures (often symplectic) and instances with no open sector. The work connects these Gepner-based constructions to duality pictures (F-theory, heterotic on $T^2$) and to potential four-dimensional ${N}=1$ vacua, illustrating a rich and testable landscape of Type I vacua arising from rational conformal field theories.

Abstract

We construct open descendants of Gepner models, concentrating mainly on the six-dimensional case, where they give type I vacua with rich patterns of Chan-Paton symmetry breaking and various numbers of tensor multiplets, including zero. We also relate the models in $D < 10$ without open sectors, recently found by other authors, to the generalized Klein-bottle projections allowed by the crosscap constraint.