Yan Gobeil, Alexander Maloney, Gim Seng Ng, Jieqiang Wu
SciPost Phys. 7, 015 (2019) ·
published 1 August 2019

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We study conformal blocks for thermal onepointfunctions on the sphere in
conformal field theories of general dimension. These thermal conformal blocks
satisfy second order Casimir differential equations and have integral
representations related to AdS Witten diagrams. We give an analytic formula for
the scalar conformal block in terms of generalized hypergeometric functions. As
an application, we deduce an asymptotic formula for the threepoint coeffcients
of primary operators in the limit where two of the operators are heavy.
SciPost Phys. 6, 065 (2019) ·
published 7 June 2019

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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.