Holographic study of heavy quark potential, free energy, and running coupling in backgrounds with broken translational symmetry
We study heavy-quark observables including static interquark potential, thermal free energy and running coupling via a five-dimensional asymptotically AdS spacetime with translational symmetry breaking (TSB). The Einstein-Maxwell-axion geometry involves two scales: chemical potential $\mu$ for finite baryon density, and TSB parameter $\beta$ for momentum relaxation. Numerical simulations at finite and zero temperature reveal that both $\mu$ and $\beta$ weaken color interactions and facilitate quarkonium dissociation in strongly coupled quark-gluon plasmas through different mechanisms. The chemical potential dominates color screening and modifies the heavy-quark potential and running coupling, while $\beta$ mainly affects plasma entropy and corrects thermal free energy. At zero temperature, thermal contributions vanish, and the renormalized free energy becomes a medium-modified static potential with an approximate Coulombic form. Finite baryon density suppresses $Q\bar{Q}$ binding much more strongly than momentum dissipation at all temperatures. We extract the color screening length and dissociation scale, and discuss phenomenological implications for quarkonium in heavy-ion collisions. This work clarifies medium correction mechanisms for color interactions and thermodynamics, and presents a consistent picture for heavy-quark probes in dense dissipative plasmas.