Abstract
Even for holographic theories that obey boundary causality, the full bulk Lorentzian path integral includes metrics that violate this condition. This leads to the following puzzle: the commutator of two field theory operators at space-like-separated points on the boundary must vanish. However, if these points are causally related in a bulk metric, then the bulk calculation of the commutator will be nonzero. It would appear that the integral over all metrics of this commutator must vanish exactly for holography to hold. This is puzzling since it must also be true if the commutator is multiplied by any other operator. Upon a careful treatment of boundary conditions in holography, we show how the bulk path integral leads to a natural resolution of this puzzle.
Highlights
Introduction.—A bulk description of nonperturbative quantum gravity is not yet available
We begin with a Lorentzian formulation of holography, in which one integrates over asymptotically anti-de Sitter (AdS) spacetimes and matter fields to compute correlation functions in a dual quantum field theory
Two boundary points that are spacelike-separated on the boundary can be timelike-separated with respect to some bulk metrics
Summary
Introduction.—A bulk description of nonperturbative quantum gravity is not yet available. In full quantum gravity (finite N), the bulk path integral includes metrics that violate boundary causality.
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