SciPost Phys. 3, 016 (2017) ·
published 28 August 2017
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· pdf
We revisit the holographic construction of (approximately) local bulk
operators inside an eternal AdS black hole in terms of operators in the
boundary CFTs. If the bulk operator carries charge, the construction must
involve a qualitatively new object: a Wilson line that stretches between the
two boundaries of the eternal black hole. This operator - more precisely, its
zero mode - cannot be expressed in terms of the boundary currents and only
exists in entangled states dual to two-sided geometries, which suggests that it
is a state-dependent operator. We determine the action of the Wilson line on
the relevant subspaces of the total Hilbert space, and show that it behaves as
a local operator from the point of view of either CFT. For the case of three
bulk dimensions, we give explicit expressions for the charged bulk field and
the Wilson line. Furthermore, we show that when acting on the thermofield
double state, the Wilson line may be extracted from a limit of certain standard
CFT operator expressions. We also comment on the relationship between the
Wilson line and previously discussed mirror operators in the eternal black
hole.
