Shape dependence of mutual information in the OPE limit: linear responses
arXiv:2207.05268 · doi:10.1007/JHEP10(2022)101
Abstract
Mutual information serves as an important measure of correlation between subsystem components. In the framework of quantum field theories (QFTs) they have better regulated UV behavior than entanglement entropy, and thus provide more direct access to universal aspects of entanglement structures. In this paper, we study the linear responses under shape deformation of the mutual information in the conformal field theory (CFT) vacuum between two spheres of radius separated by large distance or conformally equivalent configurations. Our calculations make use of the previous OPE results for mutual information \cite{Faulkner2016Aug} and the associated modular Hamiltonian \cite{Faulkner2021Aug}. In particular, we apply the entanglement first law to compute the linear responses of mutual information under shape deformation on one of the spheres. We find that the linear responses exhibit a high degree of universality for a selected class of OPE contributions. We demonstrate that there is a "little group" of symmetries associated with the set-up. Our result implies that the spherical mutual information is extremal over shape deformations of non-zero modes under the symmetry group.
arXiv comment37 pages, minor revision
References in corpus (36)
- Gauge Theory Correlators from Non-Critical String Theory
- The Large N Limit of Superconformal Field Theories and Supergravity
- A computable measure of entanglement
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Topological entanglement entropy
- Detecting topological order in a ground state wave function
- A Covariant Holographic Entanglement Entropy Proposal
- The logarithmic negativity: A full entanglement monotone that is not convex
- Towards a derivation of holographic entanglement entropy
- Implications of Conformal Invariance in Field Theories for General Dimensions
- Holographic c-theorems in arbitrary dimensions
- Spinning Conformal Correlators
- Gravitation from Entanglement in Holographic CFTs
- Remarks on entanglement entropy for gauge fields
- Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
- A comparison of entanglement measures
- Decomposition of entanglement entropy in lattice gauge theory
- Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition
- Universal terms for the entanglement entropy in 2+1 dimensions
- Remarks on the entanglement entropy for disconnected regions
- AdS/CFT and Strong Subadditivity of Entanglement Entropy
- Reduced density matrix and internal dynamics for multicomponent regions
- A Proof of the Conformal Collider Bounds
- Nonlinear Gravity from Entanglement in Conformal Field Theories
- A General Proof of the Quantum Null Energy Condition
- Some Results on Mutual Information of Disjoint Regions in Higher Dimensions
- Bulk Emergence and the RG Flow of Entanglement Entropy
- Entanglement entropy across a deformed sphere
- Entanglement Entropy: A Perturbative Calculation
- Some results on the shape dependence of entanglement and Rényi entropies
- Entanglement Entropy for Relevant and Geometric Perturbations
- Quantum Corrections to Holographic Mutual Information
- The Holographic Shape of Entanglement and Einstein's Equations
- Mutual information superadditivity and unitarity bounds
- On the Mutual Information in Conformal Field Theory
- Scattering strings off quantum extremal surfaces