No ensemble averaging below the black hole threshold

A bstract In the AdS/CFT correspondence, amplitudes associated to connected bulk manifolds with disconnected boundaries have presented a longstanding mystery. possible interpretation is that they reflect effects of averaging over an ensemble boundary theories. But in examples dimension D ≥ 3, appropriate theories does not exist. Here we sharpen puzzle by identifying class “fixed energy” or “sub-threshold” observables claim do show averaging. These are involve states above ground state only fixed amount large N limit, and particular far from being black hole states. To support our claim, explore example = solutions Einstein’s equations never contribute these observables. demonstrate this requires some novel results about renormalized volume hyperbolic three-manifold, which prove using modern methods geometry. Why then any apparent averaging? We propose reflects chaotic nature physics fact Hilbert space describing limit.