Emergent Times in Holographic Duality

Abstract

In holographic duality an eternal AdS black hole is described by two copies of the boundary CFT in the thermal eld double state. In this thesis we provide explicit constructions in the boundary theory of infalling time evolutions which can take bulk observers behind the horizon. The constructions also help to illuminate the boundary emergence of the black hole horizons, the interiors, and the associated causal structure. A key element is the emergence, in the large N limit of the boundary theory, of a type III1 von Neumann algebraic structure from the type I boundary operator algebra and the half-sided modular translation structure associated with it. A by-product is a concept called causal connectability, which is a criterion for any two quantum systems (which do not need to have a known gravity dual) to have an emergent sharp horizon structure.