Entanglement entropy in two dimensional string theory

Abstract

To understand an emergent spacetime is to understand the emergence of locality. Entanglement entropy is a powerful diagnostic of locality, because locality leads to a large amount of short distance entanglement. Two dimensional string theory is among the very simplest instances of an emergent spatial dimension. We compute the entanglement entropy in the large $N$ matrix quantum mechanics dual to two dimensional string theory, in the semiclassical limit of weak string coupling. We isolate a logarithmically large, but finite, contribution that corresponds to the short distance entanglement of the tachyon field in the emergent spacetime. From the spacetime point of view, the entanglement is regulated by a nonperturbative `graininess' of space.

1+15 pages

References in corpus (4)

• Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
• Quantum Noise as an Entanglement Meter
• The entanglement entropy of one-dimensional gases
• Random matrices and entanglement entropy of trapped Fermi gases

Cited by in corpus (41)

• Open Strings On The Rindler Horizon
• Entanglement branes in a two-dimensional string theory
• Notes on Matrix Models
• Entanglement and relative entropies for low-lying excited states in inhomogeneous one-dimensional quantum systems
• Gauge Invariant Target Space Entanglement in D-Brane Holography
• Deep Quantum Geometry of Matrices
• Bulk Entanglement Entropy and Matrices
• Areas and entropies in BFSS/gravity duality
• Target space entanglement in Matrix Models
• Target Space Entanglement Entropy
• Quantum Quench in Non-relativistic Fermionic Field Theory: Harmonic traps and 2d String Theory
• Ryu-Takayanagi Area as an Entanglement Edge Term
• Matrix Quantum Mechanics from Qubits
• Entanglement in the Quantum Hall Matrix Model
• Entanglement Renormalization and Two Dimensional String Theory
• Matrix Entanglement
• A model with no firewall
• Target space entanglement in quantum mechanics of fermions and matrices
• Entanglement entropy and the large $N$ expansion of two-dimensional Yang-Mills theory
• Correlations vs connectivity in R-charge
• Finite Entanglement Entropy of Black Holes
• Quantum Entanglement on Black Hole Horizons in String Theory and Holography
• Finiteness of Entanglement Entropy in Collective Field Theory
• Entanglement Entropy in Internal Spaces and Ryu-Takayanagi Surfaces
• Holographic Space-time Models in $1+1$ Dimensions
• Microscopic Models of Linear Dilaton Gravity and Their Semi-classical Approximations
• Emergent Area Laws from Entangled Matrices
• Replica trick and string winding
• Finite entanglement entropy and spectral dimension in quantum gravity
• Hagedorn transition and topological entanglement entropy
• A perturbative expansion for entanglement entropy in string theory
• Left-Right Entanglement Entropy for a Dp-brane with Dynamics and Background Fields
• Entanglement Entropy and Phase Space Density: Lowest Landau Levels and 1/2 BPS states
• Target Space Entanglement in Quantum Mechanics of Fermions and Matrices
• Entanglement entropy, scale-dependent dimensions and the origin of gravity
• Quantum curves as quantum distributions
• Quantum Quench in $c=1$ Matrix Model and Emergent Space-times
• Ensemble averaging in JT gravity from entanglement in Matrix Quantum Mechanics
• Collective field theory of gauged multi-matrix models: Integrating out off-diagonal strings
• Target space entanglement in quantum mechanics of fermions at finite temperature
• Scrambling and the black hole atmosphere