Wilsonian Dark Matter in String Derived $Z^\prime$ Model

The dark matter issue is among the most perplexing in contemporary physics. The problem is more enigmatic due to the wide range of possible solutions, ranging from the ultra-light to the super-massive. String theory gives rise to plausible dark matter candidates due to the breaking of the non--Abelian Grand Unified Theory (GUT) symmetries by Wilson lines. The physical spectrum then contains states that do not satisfy the quantisation conditions of the unbroken GUT symmetry. Given that the Standard Model states are identified with broken GUT representations, and provided that any ensuing symmetry breaking is induced by components of GUT states, leaves a remnant discrete symmetry that forbid the decay of the Wilsonian states. A class of such states are obtained in a heterotic-string derived $Z^\prime$ model. The model exploits the spinor-vector duality symmetry, observed in the fermionic $Z_2\times Z_2$ heterotic-string orbifolds, to generate a $Z^\prime\in E_6$ symmetry that may remain unbroken down to low energies. The $E_6$ symmetry is broken at the string level with discrete Wilson lines. The Wilsonian dark matter candidates in the string derived model are $SO(10)$, and hence Standard Model, singlets and possess non-$E_6$ $U(1)_{Z^\prime}$ charges. Depending on the $U(1)_{Z^\prime}$ breaking scale and the reheating temperature they give rise to different scenarios for the relic abundance, and in accordance with the cosmological constraints.