On pp wave limit for $ \eta $ deformed superstrings

In this paper, based on the notion of plane wave string/gauge theory duality, we explore the pp wave limit associated with the bosonic sector of $\eta$ deformed superstrings propagating in $(AdS_5 \times S^{5})_{\eta}$. Our analysis reveals that in the presence of NS-NS and RR fluxes, the pp wave limit associated to full ABF background satisfies type IIB equations in its standard form. However, the beta functions as well as the string Hamiltonian start receiving non trivial curvature corrections as one starts probing beyond pp wave limit which thereby takes solutions away from the standard type IIB form. Furthermore, using \textit{uniform} gauge, we also explore the BMN dynamics associated with short strings and compute the corresponding Hamiltonian density. Finally, we explore the Penrose limit associated with the HT background and compute the corresponding stringy spectrum for the bosonic sector.