Discrete Gauge Symmetries in Discrete MSSM-like Orientifolds

TL;DR

This study shows that discrete ${Z}_N$ gauge symmetries can emerge as remnants of open-string $U(1)$s in Gepner-model orientifolds, with potential implications for MSSM baryon and lepton stability. The authors construct an explicit integral basis for axion–U(1) couplings across all simple-current MIPFs and orientifolds of the 168 Gepner models (32990 viable orientifolds), enabling a practical readout of unbroken discrete symmetries via BF couplings and axion periodicities. An algorithm yields the integral basis and demonstrates its realization in RCFT boundary states; applied to MSSM-like spectra (UUUU and USUU) and certain SU(5) GUT models, they identify rare but nonzero instances of ${Z}_2$ and ${Z}_3$ symmetries that can forbid dangerous MSSM operators, while respecting Yukawas and mass terms. The results indicate that discrete gauge symmetries are a non-generic but viable feature in this string landscape, with tadpole-consistency constraints enhancing the incidence in some sub-classes; these findings provide a string-theoretic origin for R-parity and related symmetries with implications for low-energy phenomenology and LHC signatures.

Abstract

Motivated by the necessity of discrete Z_N symmetries in the MSSM to insure baryon stability, we study the origin of discrete gauge symmetries from open string sector U(1)'s in orientifolds based on rational conformal field theory. By means of an explicit construction, we find an integral basis for the couplings of axions and U(1) factors for all simple current MIPFs and orientifolds of all 168 Gepner models, a total of 32990 distinct cases. We discuss how the presence of discrete symmetries surviving as a subgroup of broken U(1)'s can be derived using this basis. We apply this procedure to models with MSSM chiral spectrum, concretely to all known U(3)xU(2)xU(1)xU(1) and U(3)xSp(2)xU(1)xU(1) configurations with chiral bi-fundamentals, but no chiral tensors, as well as some SU(5) GUT models. We find examples of models with Z_2 (R-parity) and Z_3 symmetries that forbid certain B and/or L violating MSSM couplings. Their presence is however relatively rare, at the level of a few percent of all cases.