Holographic Entanglement Entropy of Local Quenches in AdS${}_4$/CFT${}_3$: A Finite-Element Approach

Abstract

Understanding quantum entanglement in interacting higher-dimensional conformal field theories is a challenging task, as direct analytical calculations are often impossible to perform. With holographic entanglement entropy, calculations of entanglement entropy turn into a problem of finding extremal surfaces in a curved spacetime, which we tackle with a numerical finite-element approach. In this paper, we compute the entanglement entropy between two half-spaces resulting from a local quench, triggered by a local operator insertion in a CFT${}_3$. We find that the growth of entanglement entropy at early time agrees with the prediction from the first law, as long as the conformal dimension $\Delta$ of the local operator is small. Within the limited time region that we can probe numerically, we observe deviations from the first law and a transition to sub-linear growth at later time. In particular, the time dependence at large $\Delta$ shows qualitative differences to the simple logarithmic time dependence familiar from the CFT${}_2$ case. We hope that our work will motivate further studies, both numerical and analytical, on entanglement entropy in higher dimensions.

35 pages, 15 figures

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• Universal Local Operator Quenches and Entanglement Entropy
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