Entanglement Entropy, Relative Entropy and Duality

Abstract

A definition for the entanglement entropy in both Abelian and non-Abelian gauge theories has been given in the literature, based on an extended Hilbert space construction. The result can be expressed as a sum of two terms, a classical term and a quantum term. It has been argued that only the quantum term is extractable through the processes of quantum distillation and dilution. Here we consider gauge theories in the continuum limit and argue that quite generically, the classical piece is dominated by modes with very high momentum, of order the cut-off, in the direction normal to the entangling surface. As a result, we find that the classical term does not contribute to the relative entropy or the mutual information, in the continuum limit, for states which only carry a finite amount of energy above the ground state. We extend these considerations for $p$-form theories, and also discuss some aspects pertaining to electric-magnetic duality.

arXiv comment21 pages, 2 figures; v2: includes additional comments, matches the published version in JHEP

References in corpus (29)

• Soft Hair on Black Holes
• Notes on Some Entanglement Properties of Quantum Field Theory
• Local subsystems in gauge theory and gravity
• Superrotation Charge and Supertranslation Hair on Black Holes
• Entanglement entropy of electromagnetic edge modes
• Entanglement entropy in gauge theories and the holographic principle for electric strings
• On The Entanglement Entropy For Gauge Theories
• Entanglement entropy and nonabelian gauge symmetry
• Aspects of Entanglement Entropy for Gauge Theories
• Black Hole Entropy and Soft Hair
• Local phase space and edge modes for diffeomorphism-invariant theories
• The entanglement of distillation for gauge theories
• Lorentz-diffeomorphism edge modes in 3d gravity
• Edge Dynamics from the Path Integral: Maxwell and Yang-Mills
• Entanglement Entropy in (3+1)-d Free $U(1)$ Gauge Theory
• Entwinement in discretely gauged theories
• Scalar Asymptotic Charges and Dual Large Gauge Transformations
• Edge State Quantization: Vector Fields in Rindler
• Entanglement in Four-Dimensional SU(3) Gauge Theory
• Entanglement Entropy in 2D Non-abelian Pure Gauge Theory
• Revisiting Entanglement Entropy of Lattice Gauge Theories
• Entanglement and Thermal Entropy of Gauge Fields
• Quantum Entanglement of Locally Excited States in Maxwell Theory
• Superselection Sectors of Gravitational Subregions
• Entanglement in Weakly Coupled Lattice Gauge Theories
• Entanglement entropy, dualities, and deconfinement in gauge theories
• On the Entanglement Entropy of Maxwell Theory: A Condensed Matter Perspective
• Entanglement entropy for pure gauge theories in 1+1 dimensions using the lattice regularization
• Gauge choices and Entanglement Entropy of two dimensional lattice gauge fields

Cited by in corpus (8)

• On the logarithmic coefficient of the entanglement entropy of a Maxwell field
• Hyperbolic cylinders and entanglement entropy: gravitons, higher spins, $p$-forms
• Duality transformations and the entanglement entropy of gauge theories
• Entanglement entropy and non-local duality: quantum channels and quantum algebras
• Dynamical Edge Modes in $p$-form Gauge Theories
• Heterotic Strings and Quantum Entanglement
• Partition functions of $p$-forms from Harish-Chandra characters
• Gravitons on Nariai Edges