Holographic insights and puzzles

Abstract: The talk is composed of two parts, both set within the AdS/CFT context. In the first part, I discuss holographic insight into strongly coupled field theory in a black hole background. I conjecture two new gravitational solutions, dubbed black funnels and black droplets, which describe two distinct deconfined phases in the field theory at finite temperature. I also briefly mention puzzles associated with an analogous set-up in a rotating black hole background. In the second part of the talk, I discuss time-dependent states in a CFT on flat spacetime background, exemplified by the conformal soliton flow. Here I focus on puzzles regarding the nature of entropy in time-evolving states and its holographic dual.