Poincare Recurrences and Topological Diversity

Finite entropy thermal systems undergo Poincare recurrences. In the contextof field theory, this implies that at finite temperature, timelike two-pointfunctions will be quasi-periodic. In this note we attempt to reproduce thisbehavior using the AdS/CFT correspondence by studying the correlator of amassive scalar field in the bulk. We evaluate the correlator by summing overall the SL(2,Z) images of the BTZ spacetime. We show that all the terms in thissum receive large corrections after at certain critical time, and that theresult, even if convergent, is not quasi-periodic. We present several argumentsindicating that the periodicity will be very difficult to recover without anexact re-summation, and discuss several toy models which illustrate this.Finally, we consider the consequences for the information paradox.Comment: 18 + 8 pages, 5 figures. v2: reference adde