Thermal Width of the $\Upsilon$ at Large t' Hooft Coupling

We use the AdS/CFT correspondence to show that the heavy quark (static) potential in a strongly-coupled plasma develops an imaginary part at finite temperature. Thus, deeply bound heavy quarkonia states acquire a small nonzero thermal width when the t'Hooft coupling $\lambda=g^2 N_c \gg 1$ and the number of colors $N_c \to \infty$. In the dual gravity description, this imaginary contribution comes from thermal fluctuations around the bottom of the classical sagging string in the bulk that connects the heavy quarks located at the boundary. We predict a strong suppression of $\Upsilon$'s in heavy-ion collisions and discuss how this may be used to estimate the initial temperature.