What Does Locality Mean in Gravity?

Fabio Iunes Sanches, University of California, Berkeley

Relativistic quantum field theory successfully describes the dynamics of fundamental interactions. One principle at the core of quantum field theory is that it is inherently local: No process can violate causality, as expected from special relativity. Formally this feature is manifested by the fact that spacelike separated operators have vanishing commutators.

Once we try to incorporate gravity, the issue of locality becomes much subtler. One way to see the conflict between the two theories is through the black hole information paradox -- which also displays the holographic property of gravity. This suggests gravity is inherently nonlocal, although an effectively local description works to a very good approximation when gravitational effects are weak.

The AdS/CFT correspondence provides a precise setting to study how local physics emerges in gravity. In particular, bulk operators in the anti-de Sitter spacetime are somehow encoded in the boundary conformal field theory. This encoding must be in such a way that locality in the bulk emerges (at least approximately) from the boundary CFT. By studying the reconstruction property of bulk operators (that is, how to express bulk operators in terms of boundary quantities), we give a definition of bulk local operators using only the CFT. We find that locality is intimately related to the quantum error correction properties of the CFT.

Abstract Author(s): Fabio Sanches