String-derived MSSM vacua with residual R symmetries

TL;DR

This paper constructs string-derived MSSM vacua with a specific residual R symmetry, Z_4^R, which enforces desirable phenomenological features like proton stability and gauge-top unification, using novel computational methods.

Contribution

It introduces the Hilbert basis method and algorithms for identifying residual symmetries in string vacua, providing explicit examples with the MSSM spectrum and Z_4^R symmetry.

Findings

Explicit string vacuum with MSSM spectrum and Z_4^R symmetry

Method for fixing moduli in a supersymmetric Minkowski vacuum

Demonstration of residual R symmetry in string-derived models

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.