Entanglement entropy and edge modes in topological string theory: I
arXiv:2010.15737
Abstract
Progress in identifying the bulk microstate interpretation of the Ryu-Takayanagi formula requires understanding how to define entanglement entropy in the bulk closed string theory. Unfortunately, entanglement and Hilbert space factorization remains poorly understood in string theory. As a toy model for AdS/CFT, we study the entanglement entropy of closed strings in the topological A-model in the context of Gopakumar-Vafa duality. We will present our results in two separate papers. In this work, we consider the bulk closed string theory on the resolved conifold and give a self-consistent factorization of the closed string Hilbert space using extended TQFT methods. We incorporate our factorization map into a Frobenius algebra describing the fusion and splitting of Calabi-Yau manifolds, and find string edge modes transforming under a -deformed surface symmetry group. We define a string theory analogue of the Hartle-Hawking state and give a canonical calculation of its entanglement entropy from the reduced density matrix. Our result matches with the geometrical replica trick calculation on the resolved conifold, as well as a dual Chern-Simons theory calculation which will appear in our next paper \cite{secondpaper}. We find a realization of the Susskind-Uglum proposal identifying the entanglement entropy of closed strings with the thermal entropy of open strings ending on entanglement branes. We also comment on the BPS microstate counting of the entanglement entropy. Finally we relate the nonlocal aspects of our factorization map to analogous phenomenon recently found in JT gravity.
arXiv commentTypos corrected and citations added
References in corpus (48)
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Noncommutative Field Theory
- Eternal Black Holes in AdS
- Replica Wormholes and the Entropy of Hawking Radiation
- Black Hole Entropy in Canonical Quantum Gravity and Superstring Theory
- Introduction to string field theory
- Closed String Field Theory: Quantum Action and the BV Master Equation
- Topological Strings and Integrable Hierarchies
- Mirror Manifolds And Topological Field Theory
- Black Hole Entropy and Entropy of Entanglement
- Decomposition of entanglement entropy in lattice gauge theory
- Entanglement entropy in gauge theories and the holographic principle for electric strings
- Entanglement entropy of electromagnetic edge modes
- JT gravity as a matrix integral
- Chern-Simons Theory and Topological Strings
- Exact results for the entanglement entropy and the energy radiated by a quark
- Geometric entropy and edge modes of the electromagnetic field
- Gas of D-Branes and Hagedorn Density of BPS States
- On the structure of open-closed topological field theory in two dimensions
- The holographic dual of an EPR pair has a wormhole
- Holography, Entanglement Entropy, and Conformal Field Theories with Boundaries or Defects
- Two Dimensional Yang-Mills, Black Holes and Topological Strings
- Baby Universes in String Theory
- D-branes and K-theory in 2D topological field theory
- Entanglement in non-unitary quantum critical spin chains
- Strings on a Cone and Black Hole Entropy
- Bekenstein-Hawking Entropy as Topological Entanglement Entropy
- A mini-course on topological strings
- Baby Universes, Holography, and the Swampland
- Cobordism Classes and the Swampland
- Brane/anti-Brane Systems and U(N|M) Supergroup
- Bulk reconstruction and the Hartle-Hawking wavefunction
- Open Strings On The Rindler Horizon
- Entanglement branes in a two-dimensional string theory
- Entanglement Entropy in 2D Non-abelian Pure Gauge Theory
- Entanglement branes and factorization in conformal field theory
- Enumerative geometry of stable maps with Lagrangian boundary conditions and multiple covers of the disc
- Comments on Entanglement Entropy in String Theory
- Quantum Entanglement of Baby Universes
- Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds
- Entanglement entropy in Jackiw-Teitelboim Gravity
- Symmetry protected topological phases beyond groups: The q-deformed Affleck-Kennedy-Lieb-Tasaki model
- Origin of the quantum group symmetry in 3d quantum gravity
- Ryu-Takayanagi Area as an Entanglement Edge Term
- Curves in Calabi-Yau 3-folds and Topological Quantum Field Theory
- Entanglement Entropy in Jackiw-Teitelboim Gravity
- Entanglement entropy of Wilson loops: Holography and matrix models
- Area-dependent quantum field theory with defects