Scrambling with conservation law

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 ($d\ge 2$) 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 $\frac{d}{2}$. We also generalize the result to compute OTOCs between general operators which have overlap with the conserved charges.

24 pages, 5 figures

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• Long-time tails in the SYK chain from the effective field theory with a large number of derivatives
• Out-of-Time Ordered Correlators in Kicked Coupled Tops: Information Scrambling in Mixed Phase Space and the Role of Conserved Quantities
• Traversable wormholes via a double trace deformation involving $U(1)$ conserved current operators