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 SO(10) subgroups at the string scale, which include the flipped SU(5) ͑FSU5͒, the Pati-Salam ͑PS͒ string models, and the string standard-like models ͑SLM͒. We extend this study to include the case in which the SO(10) symmetry is broken to the left-right symmetric ͑LRS͒ gauge group, SO(10)→SU(3) C ϫU(1) BϪL ϫSU(2) L ϫSU(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 SO(10), while the weak hypercharge does not have the canonical SO(10) embedding.

NAHE-based string models with SU(4)×SU(2)×U(1) SO(10) subgroup

“…On the other hand the additional U(1) symmetries that arise from the Narain lattice can be anomalous in the LRS models and indeed LRS string models that do contain an anomalous U(1) were presented in ref. [6,11]. As we demonstrate below the SU421 models give rise to anomaly free models as well as to models that contain an anomalous U(1) symmetry.…”

“…By contrast, in the left-right symmetric models of ref. [6], and in the SU421 models, the 2γ projection breaks the SO(10) symmetry. In the FSU5, PS, SLM and LRS models, however, the 2γ projection selects complete 16 representations of SO(10) that carry different charges under the flavor U(1) symmetries, i.e.…”

“…In the observable sector the NS boundary conditions produce the generators of SU(4) C × SU(2) L × U(1) R ∈ SO(10))×U(1) 1,2,3 ×U(1) 4,5,6 , while in the hidden sector the NS boundary conditions produce the generators of…”

“…The first stage consists of the NAHE set [2,12,4] * , which is a set of five boundary condition basis vectors, {1, S, b 1 , b 2 , b 3 }. The gauge group after the NAHE set is SO(10) × SO (6) 3 × E 8 with N = 1 space-time supersymmetry. The vector S is the supersymmetry generator and the superpartners of the states from a given sector α are obtained from the sector S + α.…”

“…To date SO (10) subgroups that have been studied include the flipped SU(5) (FSU5) [2]; the standard-like models (SLM) [3,4,1]; the Pati-Salam models (PS) [5]; and the left-right symmetric models (LRS) [6]. Many of the phenomenological properties of the models naturally relate to the SO(10) subgroup which remains unbroken.…”