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arXiv · 2312.06128

On the Backreaction of Dirac Matter in JT Gravity and SYK Model

Pak Hang Chris Lau·Chen-Te Ma·Jeff Murugan·Masaki Tezuka
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Abstract

We model backreaction in AdS$_2$ JT gravity via a proposed boundary dual Sachdev-Ye-Kitaev quantum dot coupled to Dirac fermion matter and study it from the perspective of quantum entanglement and chaos. The boundary effective action accounts for the backreaction through a linear coupling of the Dirac fermions to the Gaussian-random two-body Majorana interaction term in the low-energy limit. We calculate the time evolution of the entanglement entropy between graviton and Dirac fermion fields for a separable initial state and find that it initially increases and then saturates to a finite value. Moreover, in the limit of a large number of fermions, we find a maximally entangled state between the Majorana and Dirac fields in the saturation region, implying a transition of the von Neumann algebra of observables from type I to type II. This transition in turn indicates a loss of information in the holographically dual emergent spacetime. We corroborate these observations with a detailed numerical computation of the averaged nearest-neighbor gap ratio of the boundary spectrum and provide a useful complement to quantum entanglement studies of holography.

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Pak Hang Chris Lau, Chen-Te Ma, Jeff Murugan, Masaki Tezuka. 2023-12-11. On the Backreaction of Dirac Matter in JT Gravity and SYK Model. https://doi.org/10.1016/j.physletb.2024.138702

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