A light Z′Z′ heterotic-string derived model

The existence of an extra Z′Z′ inspired from heterotic-string theory at accessible energy scales attracted considerable interest in the particle physics literature. Surprisingly, however, the construction of heterotic-string derived models that allow for an extra Z′Z′ to remain unbroken down to low scales has proven to be very difficult. The main reason being that the U(1)U(1) symmetries that are typically discussed in the literature are either anomalous or have to be broken at a high scale to generate light neutrino masses. In this paper we use for that purpose the self-duality property under the spinor vector duality, which was discovered in free fermionic heterotic string models. The chiral massless states in the self-dual models fill complete 27 representations of E6E6. The anomaly free gauge symmetry in the effective low energy field theory of our string model is SU(4)C×SU(2)L×SU(2)R×U(1)ζSU(4)C×SU(2)L×SU(2)R×U(1)ζ, where U(1)ζU(1)ζ is the family universal U(1)U(1) symmetry that descends from E6E6, and is typically anomalous in other free fermionic heterotic-string models. Our model therefore allows for the existence of a low scale Z′Z′, which is a combination of B−LB−L, U(1)ζU(1)ζ and T3RT3R. The string model is free of exotic fractionally charged states in the massless spectrum. It contains exotic SO(10)SO(10) singlet states that carry fractional, non-E6E6 charge, with respect to U(1)ζU(1)ζ. These non-E6E6 string states arise in the model due to the breaking of the E6E6 symmetry by discrete Wilson lines. They represent a distinct signature of the string vacua. They may provide viable dark matter candidates.