Entanglement entropy in Jackiw-Teitelboim gravity with matter

Abstract

In this paper, I study the entanglement entropy in Hartle-Hawking states of JT gravity set up by a Euclidean path integral with an operator inserted somewhere along the Euclidean boundary. I show that the entanglement entropy between the dual SYK models can be written to leading order in $1/G_N$ in a way that resembles a formula for entanglement entropy in a compact lattice gauge theory, but where the link that we appear to compute the entanglement across depends on where we put the operator along the Euclidean boundary. I then describe a toy model where we can write down an explicit family of density matrices whose von Neumann entropies exhibit such a phase transition as we tune an interpolating parameter. This behavior relies on a certain superselection sector structure and I comment on the possibility that the gravitational result comes from a similar emergent superselection sector structure in SYK/JT holography. The main implication is that each copy of the SYK model should then contain Hilbert space sectors labeled by multiple $SL(2,R)$ representations whose entanglement gives rise to space.

arXiv comment17+4 pages. Comments are welcome!

References in corpus (21)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Comments on the Sachdev-Ye-Kitaev model
• Generalized gravitational entropy
• Replica Wormholes and the Entropy of Hawking Radiation
• The entropy of Hawking radiation
• Chaos in AdS${}_2$ holography
• An Investigation of AdS${}_2$ Backreaction and Holography
• The Ryu-Takayanagi Formula from Quantum Error Correction
• Remarks on entanglement entropy for gauge fields
• Decomposition of entanglement entropy in lattice gauge theory
• On The Entanglement Entropy For Gauge Theories
• The Schwarzian Theory - A Wilson Line Perspective
• Physics at the entangling surface
• Bekenstein-Hawking Entropy as Topological Entanglement Entropy
• Supergroup Structure of Jackiw-Teitelboim Supergravity
• Entanglement entropy in Jackiw-Teitelboim Gravity
• Ryu-Takayanagi Area as an Entanglement Edge Term
• Edge modes without edge modes
• Building up spacetime with quantum entanglement II: It from BC-bit
• Entanglement Entropy in Jackiw-Teitelboim Gravity
• Entanglement entropy and edge modes in topological string theory: I

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