String-derived MSSM vacua with residual R symmetries

Understand

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.