Real time response on dS₃: the Topological AdS Black Hole and the Bubble

We study real time correlators in strongly coupled N=4 supersymmetric Yang-Mills theory on dS_3 x S^1, with antiperiodic boundary conditions for fermions 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 the Son- Starinets recipe in this background we compute retarded glueball propagators which exhibit an infinite set of poles yielding the quasinormal frequencies of the topological black hole. The imaginary parts of the propagators exhibit thermal effects associated with the Gibbons-Hawking temperature due to the cosmological horizon of the de Sitter boundary. We also obtain R-current correlators and find that after accounting for a small subtlety, the Son-Starinets prescription yields the retarded Green's functions. The correlators do not display diffusive behaviour at late times. Below the critical value of the circle radius, the topological black hole decays to the AdS_5 "bubble of nothing". Using a high frequency WKB approximation, we show that glueball correlators in this phase exhibit poles on the real axis. The tunnelling from the black hole to the bubble is interpreted as a hadronization transition.