We show that open strings living on a D-brane which lies outside an AdS black hole can tunnel into the black hole through worldsheet instantons. These instantons have a simple interpretation in terms of thermal quarks in the dual Yang-Mills (YM) theory. As an application we calculate the width of a meson in a strongly coupled quark-gluon plasma which is described holographically as a massless mode on a D7 brane in AdS_5 times S_5. While the width of the meson is zero to all orders in the 1/sqrt{lambda} expansion with lambda the t Hooft coupling, it receives non-perturbative contributions in 1/sqrt{lambda} from worldsheet instantons. We find that the width increases quadratically with momentum at large momentum and comment on potential phenomenological implications of this enhancement for heavy ion collisions. We also comment on how this non-perturbative effect has important consequences for the phase structure of the YM theory obtained in the classical gravity limit.
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