## SciPost Submission Page

# On the construction of charged operators inside an eternal black hole

### by Monica Guica, Daniel L. Jafferis

#### - Published as SciPost Phys. 3, 016 (2017)

### Submission summary

As Contributors: | Monica Guica |

Arxiv Link: | http://arxiv.org/abs/1511.05627v2 |

Date accepted: | 2017-08-02 |

Date submitted: | 2017-07-27 |

Submitted by: | Guica, Monica |

Submitted to: | SciPost Physics |

Domain(s): | Theoretical |

Subject area: | High-Energy Physics - Theory |

### Abstract

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.

###### Current status:

### Ontology / Topics

See full Ontology or Topics database.### Author comments upon resubmission

- 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.