Scrambling with conservation law

Gong Cheng; Brian Swingle

doi:10.1007/jhep11(2021)174

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arXiv · 2103.07624

Scrambling with conservation law

Gong Cheng·Brian Swingle

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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 ($d\geq 2$) 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.

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Gong Cheng, Brian Swingle. 2021-03-13. Scrambling with conservation law. https://doi.org/10.1007/jhep11(2021)174

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