Speaker
Souvik Banerjee
(Groningen University)
Description
We consider the algebra of simple operators defined in a
time band in a CFT with a holographic dual. The action of
these operators on the CFT vacuum can generate all low
energy states in the CFT, and no operator within the algebra
can annihilate the vacuum. For a time band smaller than the
light crossing time of AdS, local excitations within the
causal diamond in the centre of AdS are invisible to the
algebra of simple operators on the boundary by causality.
However, we show that if one goes beyond this algebra by
considering all possible boundary operators inside the time
band, it is possible to reconstruct local physics inside the
diamond as well. Our construction therefore provides a toy
model of black hole complementarity. This not only proves
that such non-locality is a fundamental feature of quantum
gravity that holds even in empty space, but also shows that
the distinction between simple and complicated operators is
a crucial feature of the approximate emergence of locality.
