Time-dependent heavy-quark potential at finite temperature from gauge-gravity duality
The potential between a heavy quark and an antiquark inside the quark-gluon plasma is studied on the basis of the gauge-gravity duality. A real-time complex potential ${V}_{Q\overline{Q}}(t,r)$ is derived from the Wilson loop, which is evaluated by its gravity dual in the Euclidean five-dimensional anti--de Sitter black hole metric. To make the analytic continuation from the imaginary time to the real time, specific variational configurations of the string world sheet in the Euclidean metric are introduced. A rapid approach of ${V}_{Q\overline{Q}}(t,r)$ to its stationary value is found at the time scale $t\ensuremath{\simeq}(\ensuremath{\pi}T{)}^{\ensuremath{-}1}$, and the imaginary part of ${V}_{Q\overline{Q}}(\ensuremath{\infty},r)$ becomes significant above the length scale $r=1.72(\ensuremath{\pi}T{)}^{\ensuremath{-}1}$. Also, these scales are independent of the 't Hooft coupling $\ensuremath{\lambda}$. Implications of these results to the properties of heavy quarkonia in quark-gluon plasma are briefly discussed.