Abstract
Recently it was shown that there is a unique Z 4 R symmetry for the MSSM which allows for the Yukawa couplings and dimension five neutrino mass operator, forbids the μ 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.
Highlights
There are many independent observations hinting at the relevance of a high scale for particle physics
Stabilizing the electroweak scale against the see-saw scale seems to require supersymmetry; remarkably, the simplest supersymmetric extension of the standard model, the MSSM, realizes the compelling scenario of gauge unification [2] at a scale MGUT 2 · 1016 GeV, which is suspiciously close to the see-saw scale
We focus on “maximal vacua”, i.e. we assume that all fields which are neutral under the remnant gauge and discrete symmetries, called φ(i) (1 i N ) in what follows, attain vacuum expectation values (VEVs)
Summary
There are many independent observations hinting at the relevance of a high scale for particle physics. There is the so-called doublet–triplet splitting, and related to it, the MSSM μ problem Even if this problem is solved, unified models typically are in conflict with dimension five proton decay [3,4] operators. (It is well known that dimension four proton decay can be forbidden by matter parity.1) Third, in four-dimensional models of grand unification there is no relation between the GUT and Planck scales, MGUT and MP. The role of discrete symmetries in identifying and analyzing such vacua has been stressed recently [17] One of these symmetries is matter parity, which has been successfully embedded in string theory [16]. It commutes with SO(10) in the matter sector This symmetry has the appealing feature that it forbids automatically dimension four and five proton decay operators.
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