In a paper today, with Chandramouli Chowdhury, Victor Godet and Olga Papadoulaki, we establish a link between two famous but seemingly different approaches to quantum gravity. On one hand, we have the Wheeler-DeWitt (WDW) equation that was first written down more than 50 years ago. On the other hand, we have now known for almost 25 years that gravitational theories in anti-de Sitter space (AdS) are holographic, and this has been an extraordinarily fruitful idea.
In today’s paper, we show that a version of holography can be derived from the WDW equation. More precisely we show, within perturbation theory, that two wavefunctionals that solve the WDW equation in AdS, and coincide at the boundary of AdS for an infinitesimal time interval, must coincide everywhere in the bulk.
Contrast this with ordinary quantum field theories (QFTs) where it is obvious that one can prepare states that coincide outside a bounded region but differ inside. This is why, in ordinary QFTs, information is stored locally. The result today shows that the WDW equation prevents the existence of such “split states” in quantum gravity and that information in gravitational wavefunctionals can be always be found near the boundary of a Cauchy slice.
Our analysis is perturbative but several separate arguments that we have given over the last couple of years, for the “principle of holography of information” in gravity, suggest that the final result should extend beyond perturbation theory.
Read more at: https://arxiv.org/pdf/2107.14802.pdf
