Entanglement entropy and edge modes in topological string theory II: The dual gauge theory story

Abstract

This is the second in a two-part paper devoted to studying entanglement entropy and edge modes in the A model topological string theory. This theory enjoys a gauge-string (Gopakumar-Vafa) duality which is a topological analogue of AdS/CFT. In part 1, we defined a notion of generalized entropy for the topological closed string theory on the resolved conifold. We provided a canonical interpretation of the generalized entropy in terms of the q-deformed entanglement entropy of the Hartle-Hawking state. We found string edge modes transforming under a quantum group symmetry and interpreted them as entanglement branes. In this work, we provide the dual Chern-Simons gauge theory description. Using Gopakumar-Vafa duality, we map the closed string theory Hartle-Hawking state to a Chern-Simons theory state containing a superposition of Wilson loops. These Wilson loops are dual to closed string worldsheets that determine the partition function of the resolved conifold. We show that the undeformed entanglement entropy due to cutting these Wilson loops reproduces the bulk generalized entropy and therefore captures the entanglement underlying the bulk spacetime. Finally, we show that under the Gopakumar-Vafa duality, the bulk entanglement branes are mapped to a configuration of topological D-branes, and the non-local entanglement boundary condition in the bulk is mapped to a local boundary condition in the gauge theory dual. This suggests that the geometric transition underlying the gauge-string duality may also be responsible for the emergence of entanglement branes.

typos corrected, updated the conclusion and discussion of the defect operator in section 2.5, one new figure, and references added

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• The Refined Topological Vertex
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Holographic Wilson Loops
• Two Dimensional Yang-Mills, Black Holes and Topological Strings
• Global symmetry, Euclidean gravity, and the black hole information problem
• Quantum Entanglement of Baby Universes
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• Interfaces and the extended Hilbert space of Chern-Simons theory
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Cited by in corpus (8)

• Edge modes as reference frames and boundary actions from post-selection
• A proposal for 3d quantum gravity and its bulk factorization
• Matrix Quantization of Gravitational Edge Modes
• A note on the bulk interpretation of the Quantum Extremal Surface formula
• Hartle-Hawking state and its factorization in 3d gravity
• Dynamical Edge Modes in $p$-form Gauge Theories
• Ryu-Takayanagi Formula for Multi-Boundary Black Holes from 2D Large-$c$ CFT Ensemble
• Minimal Factorization of Chern-Simons Theory -- Gravitational Anyonic Edge Modes