Entanglement branes and factorization in conformal field theory
arXiv:1912.11201 · doi:10.1103/PhysRevD.104.026012
Abstract
In this work, we consider the question of local Hilbert space factorization in 2D conformal field theory. Generalizing previous work on entanglement and open-closed TQFT, we interpret the factorization of CFT states in terms of path integral processes that split and join the Hilbert spaces of circles and intervals. More abstractly, these processes are cobordisms of an extended CFT which are defined purely in terms of the OPE data. In addition to the usual sewing axioms, we impose an entanglement boundary condition that is satisfied by the vacuum Ishibashi state. This choice of entanglement boundary state leads to reduced density matrices that sum over super-selection sectors, which we identify as the CFT edge modes. Finally, we relate our factorization map to the co-product formula for the CFT symmetry algebra, which we show is equivalent to a Boguliubov transformation in the case of a free boson.
arXiv commentCitations and footnote 1 added
References in corpus (28)
- Aspects of AdS/BCFT
- Local subsystems in gauge theory and gravity
- Remarks on entanglement entropy for gauge fields
- Completeness Conditions for Boundary Operators in 2D Conformal Field Theory
- Entanglement entropy in gauge theories and the holographic principle for electric strings
- Entanglement entropy and nonabelian gauge symmetry
- Conformal boundary states for free bosons and fermions
- Physics at the entangling surface
- D-branes and K-theory in 2D topological field theory
- Open-closed strings: Two-dimensional extended TQFTs and Frobenius algebras
- Bose-Fermi duality and entanglement entropies
- Disk entanglement entropy for a Maxwell field
- On the Non-commutativity of Closed String Zero Modes
- Intrinsic non-commutativity of closed string theory
- Scalar Asymptotic Charges and Dual Large Gauge Transformations
- Matrix product states and equivariant topological field theories for bosonic symmetry-protected topological phases in (1+1) dimensions
- Geometric interpretation of the multi-scale entanglement renormalization ansatz
- Fusion in conformal field theory as the tensor product of the symmetry algebra
- Tensor networks as path integral geometry
- Entanglement entropy in Jackiw-Teitelboim Gravity
- Entanglement branes, modular flow, and extended topological quantum field theory
- Comments on Defining Entanglement Entropy
- Ryu-Takayanagi Area as an Entanglement Edge Term
- Building up spacetime with quantum entanglement II: It from BC-bit
- Tensor networks as conformal transformations
- Gluing together Modular flows with free fermions
- Entanglement Entropy in Jackiw-Teitelboim Gravity
- Entanglement Entropy and Boundary Conditions in 1+1 Dimensions
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- Multi-charged moments of two intervals in conformal field theory
- Dynamical Edge Modes and Entanglement in Maxwell Theory
- A note on the bulk interpretation of the Quantum Extremal Surface formula
- Page curve and symmetries
- A Type Approximation of the Crossed Product
- Symmetry-resolved entanglement in fermionic systems with dissipation
- Multipartite edge modes and tensor networks
- Minimal Areas from Entangled Matrices
- Dynamical Edge Modes in -form Gauge Theories
- Deriving the non-perturbative gravitational dual of quantum Liouville theory from BCFT operator algebra
- Operator-state correspondence in simple current extended conformal field theories: Toward a general understanding of chiral conformal field theories and topological orders
- Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models
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- A new look at the entanglement entropy of a single interval in a 2d CFT
- Thermodynamic symmetry resolved entanglement entropies in integrable systems