Holographic study of heavy quark potential, free energy, and running coupling in backgrounds with broken translational symmetry
Abstract
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 μ for finite baryon density, and TSB parameter β for momentum relaxation. Numerical simulations at finite and zero temperature reveal that both μ and β 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 β 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 QQ 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.