Abstract
Finite entropy thermal systems undergo Poincaré
recurrences. In the context of field theory, this implies that at
finite temperature, timelike two-point functions will be
quasi-periodic. In this note we attempt to reproduce this behavior
using the AdS/CFT correspondence by studying the correlator of a
massive scalar field in the bulk. We evaluate the correlator by
summing over all the SL(2,
) images of the BTZ
spacetime. We show that all the terms in this sum receive large
corrections after at certain critical time, and that the result,
even if convergent, is not quasi-periodic. We present several
arguments indicating that the periodicity will be very difficult to
recover without an exact re-summation, and discuss several toy
models which illustrate this. Finally, we consider the consequences
for the information paradox.
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