Quantum revivals in conformal field theories in higher dimensions

Abstract

We investigate the behavior of the return amplitude following a quantum quench in a conformal field theory (CFT) on a compact spatial manifold of dimension and linear size , from a state of extensive energy with short-range correlations. After an initial gaussian decay reaches a plateau value related to the density of available states at the initial energy. However for this value is attained from below after a single oscillation. For a holographic CFT the plateau persists up to times at least , where is the dimensionless Stefan–Boltzmann constant. On the other hand for a free field theory on manifolds with high symmetry there are typically revivals at times . In particular, on a sphere of circumference , there is an action of the modular group on implying structure near all rational values of t/L, similar to what happens for rational CFTs in .