String Constraints on Discrete Symmetries in MSSM Type II Quivers

TL;DR

This work connects four-dimensional discrete gauge anomaly constraints with string-inspired cycle constraints to assess which abelian discrete symmetries can survive in local D-brane MSSM-like models. Using a bottom-up scan of four-stack quivers consistent with tadpole and massless U(1) conditions, the authors find that family-independent ${f Z}_2$, ${f Z}_3$, and ${f Z}_6$ symmetries can arise, but family-dependent discrete symmetries do not. Proton hexality, which forbids R-parity violation and dangerous dimension-5 proton decay operators while permitting the $ ext{mu-term}$ and Weinberg operator, is realized only in a small subset of configurations and depends sensitively on the hypercharge embedding. No ${f Z}_9$ or ${f Z}_{18}$ symmetries appear in these four-stack realizations, underscoring stringy constraints beyond pure 4D anomaly considerations. The results suggest Proton hexality is relatively rare in local D-brane models, and motivate extending the analysis to more stacks or to NMSSM/GUT contexts and to symmetries from geometric isometries.

Abstract

We study the presence of discrete gauge symmetries in D-brane semi-realistic compactifications. After establishing the constraints on the transformation behaviour of the chiral matter for the presence of a discrete gauge symmetry we perform a systematic search for discrete gauge symmetries within local semi-realistic D-brane realizations, based on four D-brane stacks, of the MSSM and the MSSM with three right-handed neutrinos. The systematic search reveals that Proton hexality, a discrete symmetry which ensures the absence of R-parity violating terms as well as the absence of dangerous dimension 5 proton decay operators, is only rarely realized. Moreover, none of the semi-realistic local D-brane configurations exhibit any family dependent discrete gauge symmetry.