Schedule Oct 21, 2021
Imaging the quantum extremal surface
Adam Levine, IAS
Cite as: doi:10.26081/K6N917

I will discuss recent work on a Hayden & Preskill like setup for both maximally chaotic and sub- maximally chaotic quantum field theories. We act on the vacuum with an operator in a Rindler like wedge R and transfer a small subregion I of R to the other wedge. The chaotic scrambling dynamics of the QFT Rindler time evolution reveals the information in the other wedge. The holographic dual of this process involves a particle excitation falling into the bulk and crossing into the entanglement wedge of the complement to r = R\I. I will discuss computations of various quantum information measures on the boundary that tell us when the particle has entered this entanglement wedge. In a maximally chaotic theory, these measures indicate a sharp transition where the particle enters the wedge exactly when the insertion is null separated from the quantum extremal surface for r. For sub-maximally chaotic theories, we find a smoothed crossover at a delayed time given in terms of the smaller Lyapunov exponent and dependent on the time-smearing scale of the probe excitation. The information quantities that we will consider include the full vacuum modular energy R\I as well as the fidelity between the state with the particle and the state without. Along the way, I will discuss a new explicit formula for the modular Hamiltonian of two intervals in an arbitrary 1+1 dimensional CFT to leading order in the small cross ratio limit. I will also give an explicit calculation of the Regge limit of the modular flowed chaos correlator and find examples which do not saturate the modular chaos bound. I will discuss the extent to which our results reveal properties of the target of the probe excitation as a "stringy quantum extremal surface" or simply quantify the probe itself thus giving a new approach to studying the notion of longitudinal string spreading. Finally, if time allows, I will discuss upcoming work on the existence of quantum extremal surfaces in the bulk dual of the SYK model which are associated to a subset of SYK spins.

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