Scrambling with conservation laws

Abstract

In this article we discuss the impact of conservation laws, specifically U(1) charge conservation and energy conservation, on scrambling dynamics, especially on the approach to the late time fully scrambled state. As a model, we consider a d + 1 dimensional (d ≥ 2) holographic conformal field theory with Einstein gravity dual. Using the holographic dictionary, we calculate out-of-time-order-correlators (OTOCs) that involve the conserved U(1) current operator or energy-momentum tensor. We show that these OTOCs approach their late time value as a power law in time, with a universal exponent d2. We also generalize the result to compute OTOCs between general operators which have overlap with the conserved charges.