Black holes, heavy states, phase shift and anomalous dimensions
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 h...
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| Format: | Article |
| Language: | English |
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SciPost
2019-06-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.6.6.065 |
| Summary: | 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. |
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| ISSN: | 2542-4653 |