## SciPost Submission Page

# Black Holes, Heavy States, Phase Shift and Anomalous Dimensions

### by Manuela Kulaxizi, Gim Seng Ng, Andrei Parnachev

####
- Published as
SciPost Phys.
**6**,
65
(2019)

### Submission summary

As Contributors: | Manuela Kulaxizi · Gim Seng Ng · Andrei Parnachev |

Arxiv Link: | https://arxiv.org/abs/1812.03120v3 |

Date accepted: | 2019-05-21 |

Date submitted: | 2019-05-16 |

Submitted by: | Ng, Gim Seng |

Submitted to: | SciPost Physics |

Domain(s): | Theoretical |

Subject area: | High-Energy Physics - Theory |

### Abstract

We compute the phase shift of a highly energetic particle traveling in the background of an asymptotically AdS black hole. In the dual CFT, the phase shift is related to a four point function in the Regge limit. The black hole mass is translated to the ratio between the conformal dimension of a heavy operator and the central charge. This ratio serves as a useful expansion parameter; its power measures the number of stress tensors appearing in the intermediate channel. We compute the leading term in the phase shift in a holographic CFT of arbitrary dimensionality using Conformal Regge Theory and observe complete agreement with the gravity result. In a two-dimensional CFT with a large central charge the heavy-heavy-light-light Virasoro vacuum block reproduces the gravity phase shift to all orders in the expansion parameter. We show that the leading order phase shift is related to the anomalous dimensions of certain double trace operators and verify this agreement using known results for the latter. We also perform a separate gravity calculation of these anomalous dimensions to second order in the expansion parameter and compare with the phase shift expansion.

###### Current status:

**6**, 65 (2019)

### Ontology / Topics

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

We would like to thank the referees for their comments. In response, we made the following changes such that some aspects of the paper are clearer.

### List of changes

1. We added a paragraph at the end of Section 2.3 discussing the difference between the BTZ and the conical defect cases.

2. We added a sentence below eq. 2.39 emphasising its agreement with eq. 2.33.

3. We changed the first sentence of Section 2.3 to make it clearer.

4. We added Fig. 1 as requested by the referee.

5. We removed the first sentence below eq. 3.8 and modified the next sentence.

6. We modified the last sentence of Section 7 as requested.

7. We also capitalized “kronecker”, as requested by the referee.