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Black Holes, Heavy States, Phase Shift and Anomalous Dimensions
by Manuela Kulaxizi, Gim Seng Ng, Andrei Parnachev
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Submission summary
Authors (as registered SciPost users):  Manuela Kulaxizi · Gim Seng Ng · Andrei Parnachev 
Submission information  

Preprint Link:  https://arxiv.org/abs/1812.03120v3 (pdf) 
Date accepted:  20190521 
Date submitted:  20190516 02:00 
Submitted by:  Ng, Gim Seng 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
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 twodimensional CFT with a large central charge the heavyheavylightlight 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.
Author comments upon resubmission
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.
Published as SciPost Phys. 6, 065 (2019)