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On the construction of charged operators inside an eternal black hole

by Monica Guica, Daniel L. Jafferis

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Submission summary

Authors (as registered SciPost users): Monica Guica
Submission information
Preprint Link:  (pdf)
Date accepted: 2017-08-02
Date submitted: 2017-07-27 02:00
Submitted by: Guica, Monica
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


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.

Author comments upon resubmission

We thank the referee for his comments. We have submitted a new version of our article, with the following modifications:

  • we specified in the introduction and at the beginning of section 3.3 that the Wilson line behaves as a local operator for the particular choice of bulk curve Γ

we discuss in that section. This should address comment 2) of the referee.

  • we added at the end of section 4.3 a brief proof of state-dependence (in the strong, Papadodimas-Raju sense) of the Wilson line in the time-shifted states and commented on the relationship with the proposal of 1510.07911. This should address comment 1).

  • we also specified at the beginning of section 4.2 that we are interested in a representation of the Wilson line in terms of simple operators in the two CFTs, for which only the case of a bifurcate horizon is relevant, thus addressing comment 3).

List of changes

See comments above.

Published as SciPost Phys. 3, 016 (2017)

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