Field theory aspects of $\eta$-deformed superstring background

We explore various field theory aspects of integrable $\eta$-deformed geometry in type IIB supergravity by employing several holographic probes. These include the computation of holographic timelike entanglement entropy and estimation of various other field theory observables for example, the flow central charge and the quantum complexity. We also discuss the associated brane set up and compute Page charges. We further use them to calculate the coupling constant in the dual QFTs considering both small and large deformation limits.