Holographic computation of Wilson loops in a background with broken conformal invariance and finite chemical potential

Abstract

In this paper, we follow a `bottom-up' AdS/QCD approach to holographically probe the dynamics of a moving $q\bar{q}$ pair inside a strongly coupled plasma at the boundary. We consider a deformed AdS-Reissner Nordstr\"om metric in the bulk in order to introduce nonconformality and finite quark density in the dual field theory. By boosting the gravity solution in a specific direction we consider two extreme cases of orientation, parallel and perpendicular, for the Wilson loop which in turn fixes the relative position of the $q\bar{q}$ pair with respect to the direction of boost in the plasma. By utilizing this set-up, we holographically compute the vacuum expectation value of the time-like Wilson loop in order to obtain real part of the $q\bar{q}$ potential and the effects of nonconformality (deformation parameter $c$), chemical potential $\mu$ and rapidity $\beta$ are observed on this potential. We then compute the in-medium energy loss of the moving parton (jet quenching parameter $q_m$) by setting $\beta\rightarrow\infty$ which in turn makes the Wilson loop light-like. We also use the jet quenching as an order parameter to probe the strongly-coupled domain of the dual field theory. Finally, we compute the imaginary part of the $q\bar{q}$ potential ($\mathrm{Im}(V_{q\bar{q}})$) by considering the thermal fluctuation (arbitrary long wavelength) of the string world-sheet. It is observed that for fixed values of the chemical potential and rapidity, increase in the nonconformality parameter leads to an increase in the real and imaginary potentials as well as the jet quenching parameter.