R-parity from string compactification

Abstract

In this paper, we embed the $\Z_{4R}$ parity as a discrete subgroup of a global symmetry \UoR\,obtained from $\Z_{12-I}$ compactification of heterotic string $\EE8$. A part of \UoR\,transformation is the shift of the anticommuting variable $\vartheta$ to $e^{i\alpha}\vartheta$ which necessarily incoorporate the transformation of 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 \UoR~is defined as \UEE$\times$\UKK~where \UEE~is the part from $\EE8$ and \UKK~is the part generated by $Q_{18},Q_{20}$, and $Q_{22}$. We propose a method to define a \UoR~direction. The needed vacuum expectation values for breaking gauge U(1)'s except U(1)$_Y$ of the standard model carry \UoR~charge 4 modulo 4 such that \UoR~is broken down to $\Z_{4R}$ at the grand unification scale. $\Z_{4R}$ is broken to $\Z_{2R}$ between the intermediate ($\sim 10^{11\,}\gev$) and the electroweak scales ($100\,\gev\sim 1\,\tev$). The conditions we impose are proton longevity, a large top quark mass, and acceptable magnitudes for the $\mu$ term and neutrino masses.