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We study real time correlators in strongly coupled N=4 supersymmetricYang-Mills theory on dS_3 x S^1, with antiperiodic boundary conditions forfermions on the circle. When the circle radius is larger than a critical value,the dual geometry is the so-called "topological AdS_5 black hole". Applying theSon- Starinets recipe in this background we compute retarded glueballpropagators which exhibit an infinite set of poles yielding the quasinormalfrequencies of the topological black hole. The imaginary parts of thepropagators exhibit thermal effects associated with the Gibbons-Hawkingtemperature due to the cosmological horizon of the de Sitter boundary. We alsoobtain R-current correlators and find that after accounting for a smallsubtlety, the Son-Starinets prescription yields the retarded Green's functions.The correlators do not display diffusive behaviour at late times. Below thecritical value of the circle radius, the topological black hole decays to theAdS_5 "bubble of nothing". Using a high frequency WKB approximation, we showthat glueball correlators in this phase exhibit poles on the real axis. Thetunnelling from the black hole to the bubble is interpreted as a hadronizationtransition.

Real time response on dS_3: the Topological AdS Black Hole and the Bubble