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After revisiting the heterotic string-derived low-energy effective model of\cite{Ashfaque:2016ydg, Athanasopoulos:2014bba, Faraggi:2016xnm,Ashfaque:2016jha} constructed in the four-dimensional free fermionicformulation, we find two axions which are either harmful or massive. As adirect consequence, they can not solve the strong $CP$ problem which is incomplete agreement with \cite{Lopez:1990iq, Halyo:1993xn}. We also explore thepossibility of the self-interacting dark matter residing in the non-Abeliangauge group present in the hidden sector \cite{Faraggi:2000pv}. We find thatthe low-energy string-derived model naturally welcomes the self-interactingdark matter as $4$ copies of the non-Abelian, hidden $SU(2)$ gauge group factorare present.

Axions And Self-Interacting Dark Matter In The Heterotic String-Derived Model