R parity from string compactification

Abstract

In this paper, we embed the Z(4R) parity as a discrete subgroup of a global symmetry U(1)(R) obtained from Z(12-I) compactification of a heterotic string E-8 x E-8('). A part of U(1)(R) transformation is the shift of the anticommuting variable to v e(ia) v, which necessarily incorporates the transformation of the internal space coordinate. Out of six internal spaces, we identify three U(1)' s whose charges are denoted as Q(18), Q(20), and Q(22). The U(1)(R) is defined as U(1)(EE) xU(1)(KK), where U(1)(EE) is the part from the E-8 x E-8(') and U(1)(KK) is the part generated by Q(18), Q(20), and Q(22). We propose a method to define a Uo1thornR direction. The needed vacuum expectation values for breaking gauge U(1)' s except for U(1)(Y) of the standard model carry a U(1)(R) charge 4 modulo 4 such that Uo1thornR is broken down to Z(4R) at the grand unification scale. Z(4R) is broken to Z(2R) between the intermediate (similar to 10(11) GeV) and the electroweak scales (100 GeV similar to 1 TeV). The conditions we impose are proton longevity, a large top quark mass, and acceptable magnitudes for the mu term and neutrino masses. c.Published by the American Physical Society