Poincare Recurrences and Topological Diversity
Abstract
Finite entropy thermal systems undergo Poincaré recurrences. In the context of field theory, this implies that at finite temperature, timelike twopoint functions will be quasiperiodic. 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,Bbb Z) 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 quasiperiodic. We present several arguments indicating that the periodicity will be very difficult to recover without an exact resummation, and discuss several toy models which illustrate this. Finally, we consider the consequences for the information paradox.
 Publication:

Journal of High Energy Physics
 Pub Date:
 October 2004
 DOI:
 10.1088/11266708/2004/10/030
 arXiv:
 arXiv:hepth/0407192
 Bibcode:
 2004JHEP...10..030K
 Keywords:

 Black Holes in String Theory AdSCFT and dSCFT Correspondence Models of Quantum Gravity Black Holes;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 18 + 8 pages, 5 figures. v2: reference added