String-derived MSSM vacua with residual R symmetries

TL;DR

The paper constructs a string-derived MSSM vacuum that preserves a unique anomaly-cancelled $\mathbbm{Z}_4^R$ symmetry, which forbids the perturbative $\mu$ term and dimension-four/five proton decay operators while allowing MSSM Yukawas and neutrino masses. The authors develop and apply Hilbert-basis and remnant-symmetry techniques to systematically identify $D$-flat directions and SUSY vacua that retain $\mathbbm{Z}_4^R$, producing an exact MSSM spectrum with moduli stabilized in a perturbative Minkowski vacuum and enabling features like gauge–top unification and a $D_4$ flavor structure. The explicit model leverages a $\mathbb{Z}_2\times\mathbb{Z}_2$ heterotic orbifold with a freely acting symmetry, achieving non-local GUT breaking, suppressed non-perturbative $\mu$ generation, and full-rank Yukawas, while predicting a seesaw mechanism with 11 SM singlets and a non-perturbative violation channel for rare operators. This work provides practical, scalable tools to identify realistic, symmetry-protected vacua in string theory with potential implications for phenomenology and unification. The approach bridges high-scale theory (string compactifications) with MSSM-like phenomenology through explicit vacua and robust symmetry-based criteria.

Abstract

Recently it was shown that there is a unique Z_4^R symmetry for the MSSM which allows the Yukawa couplings and dimension five neutrino mass operator, forbids the mu term and commutes with SO(10). This Z_4^R symmetry contains matter parity as a subgroup and forbids dimension four and five proton decay operators. We show how to construct string vacua with discrete R symmetries in general and this symmetry in particular, and present an explicit example which exhibits the exact MSSM spectrum, the Z_4^R symmetry as well as other desired features such as gauge-top unification. We introduce the Hilbert basis method for determining all D-flat configurations and efficient algorithms for identifying field configurations with a desired residual symmetry. These methods are used in an explicit example, in which we describe in detail how to construct a supersymmetric vacuum configuration with the phenomenologically attractive Z_4^R symmetry. At the perturbative level, this is a supersymmetric Minkowski vacuum in which almost all singlet fields (moduli) are fixed.