AI Article Synopsis
- Holographic theories generally respect a principle called boundary causality, but the complete calculation using bulk metrics sometimes includes those that don't.
- This creates a conflict where, under normal circumstances, the commutator of two operators in field theory at space-like-separated points should equal zero, yet it doesn't when evaluated in certain bulk metrics.
- The text explores how a careful approach to boundary conditions in holography can resolve this seeming contradiction, ensuring the commutator remains zero as required for the theory to hold.
Article 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.
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| http://dx.doi.org/10.1103/PhysRevLett.127.081603 | DOI Listing |
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