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.

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

References in corpus (56)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Topological entanglement entropy
• String Theory Dynamics In Various Dimensions
• Heterotic and Type I String Dynamics from Eleven Dimensions
• Wilson loops in large N field theories
• A Covariant Holographic Entanglement Entropy Proposal
• Eternal Black Holes in AdS
• Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity
• Cool horizons for entangled black holes
• Generalized gravitational entropy
• Building up spacetime with quantum entanglement
• Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes
• Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
• Quantum corrections to holographic entanglement entropy
• Black Hole Entropy in Canonical Quantum Gravity and Superstring Theory
• Matrix Models, Topological Strings, and Supersymmetric Gauge Theories
• The Topological Vertex
• Topological Strings and Integrable Hierarchies
• The Refined Topological Vertex
• Mirror Manifolds And Topological Field Theory
• Knot Invariants and Topological Strings
• Local subsystems in gauge theory and gravity
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Quantization of Integrable Systems and Four Dimensional Gauge Theories
• Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information
• Holographic Wilson Loops
• Worldsheet Derivation of a Large N Duality
• Black Holes, q-Deformed 2d Yang-Mills, and Non-perturbative Topological Strings
• Topological Entanglement Entropy in Chern-Simons Theories and Quantum Hall Fluids
• Quantum Background Independence In String Theory
• Chern-Simons Theory and Topological Strings
• Exact results for the entanglement entropy and the energy radiated by a quark
• Quantum groups and nonabelian braiding in quantum Hall systems
• Hartle-Hawking Wave-Function for Flux Compactifications
• The holographic dual of an EPR pair has a wormhole
• Holography, Entanglement Entropy, and Conformal Field Theories with Boundaries or Defects
• All Loop Topological String Amplitudes From Chern-Simons Theory
• Two Dimensional Yang-Mills, Black Holes and Topological Strings
• Edge theory approach to topological entanglement entropy, mutual information and entanglement negativity in Chern-Simons theories
• Baby Universes in String Theory
• Global symmetry, Euclidean gravity, and the black hole information problem
• Entanglement in non-unitary quantum critical spin chains
• Universal features of left-right entanglement entropy
• Entanglement entropies of minimal models from null-vectors
• Entanglement branes in a two-dimensional string theory
• A note on entanglement edge modes in Chern Simons theory
• Quantum Entanglement of Baby Universes
• Wilson Loops, Geometric Transitions and Bubbling Calabi-Yau's
• Large-N limits of 2d CFTs, Quivers and AdS_3 duals
• Symmetry protected topological phases beyond groups: The q-deformed Affleck-Kennedy-Lieb-Tasaki model
• Entanglement branes, modular flow, and extended topological quantum field theory
• Interfaces and the extended Hilbert space of Chern-Simons theory
• Topological string entanglement
• Large N Expansion of q-Deformed Two-Dimensional Yang-Mills Theory and Hecke Algebras

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