Quantum Revivals in Conformal Field Theories in Higher Dimensions

TL;DR

This paper studies quantum revivals and return amplitudes in conformal field theories across various dimensions, revealing distinct behaviors in free and holographic theories, including revivals, plateaus, and modular structures.

Contribution

It provides a detailed analysis of quantum revivals in higher-dimensional CFTs, highlighting differences between free and holographic cases and uncovering modular structures in the return amplitude.

Findings

Revival times depend on the theory type and geometry.

Holographic CFTs exhibit long-lasting plateaus in return amplitude.

Free theories show revivals at rational times related to the manifold's symmetry.

Abstract

We investigate the behavior of the return amplitude ${\cal F}(t)= |\langle\Psi(0)|\Psi(t)\rangle|$ following a quantum quench in a conformal field theory (CFT) on a compact spatial manifold of dimension $d-1$ and linear size $O(L)$, from a state $|\Psi(0)\rangle$ of extensive energy with short-range correlations. After an initial gaussian decay ${\cal F}(t)$ reaches a plateau value related to the density of available states at the initial energy. However for $d=3,4$ this value is attained from below after a single oscillation. For a holographic CFT the plateau persists up to times at least $O(\sigma^{1/(d-1)} L)$, where $\sigma\gg1$ 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 $t\sim\mbox{integer}\times L$. In particular, on a sphere $S_{d-1}$ of circumference $2\pi L$, there is an action of the modular group on ${\cal F}(t)$ implying structure near all rational values of $t/L$, similarly to what happens for rational CFTs in $d=2$.