Left-right symmetric heterotic-string derived models

Abstract

Recently it was demonstrated that free fermionic heterotic strings can produce models with solely the minimal supersymmetric standard model states in the low energy spectrum. This unprecedented result provides further strong evidence for the possibility that the true string vacuum shares some of the properties of the free fermionic models. Past free fermionic models have focused on several possible unbroken observable $\mathrm{SO}(10)$ subgroups at the string scale, which include the flipped $\mathrm{SU}(5)$ (FSU5), the Pati-Salam (PS) string models, and the string standard-like models (SLM). We extend this study to include the case in which the $\mathrm{SO}(10)$ symmetry is broken to the left-right symmetric (LRS) gauge group, $\mathrm{SO}(10)\ensuremath{\rightarrow}{\mathrm{SU}(3)}_{C}\ifmmode\times\else\texttimes\fi{}{U(1)}_{B\ensuremath{-}L}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(2)}_{L}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(2)}_{R}.$ We present several models of this type and discuss their phenomenological features. The most striking new outcome of the LRS string models, in contrast with the case of the FSU5, the PS, and the SLM string models, is that they can produce effective field theories that are free of Abelian anomalies. We discuss the distinction between the two types of free fermionic models which result in the presence, or absence, of an anomalous $U(1).$ As a counterexample we also present a LRS model that does contain an anomalous $U(1).$ Additionally, we discuss how in string models the standard model spectrum may arise from the three $16$ representations of $\mathrm{SO}(10),$ while the weak hypercharge does not have the canonical $\mathrm{SO}(10)$ embedding.