Entanglement Entropy in (3+1)-d Free $U(1)$ Gauge Theory

Abstract

We consider the entanglement entropy for a free $U(1)$ theory in $3+1$ dimensions in the extended Hilbert space definition. By taking the continuum limit carefully we obtain a replica trick path integral which calculates this entanglement entropy. The path integral is gauge invariant, with a gauge fixing delta function accompanied by a Faddeev-Popov determinant. For a spherical region it follows that the result for the logarithmic term in the entanglement, which is universal, is given by the $a$ anomaly coefficient. We also consider the extractable part of the entanglement, which corresponds to the number of Bell pairs which can be obtained from entanglement distillation or dilution. For a spherical region we show that the coefficient of the logarithmic term for the extractable part is different from the extended Hilbert space result. We argue that the two results will differ in general, and this difference is accounted for by a massless scalar living on the boundary of the region of interest.

arXiv comment29 pages, 1 appendix

References in corpus (28)

• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Aspects of Holographic Entanglement Entropy
• Towards a derivation of holographic entanglement entropy
• Generalized gravitational entropy
• Entanglement entropy of black holes
• Form factors of branch-point twist fields in quantum integrable models and entanglement entropy
• Remarks on entanglement entropy for gauge fields
• Entanglement entropy, conformal invariance and extrinsic geometry
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• 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
• On The Entanglement Entropy For Gauge Theories
• Geometric entropy and edge modes of the electromagnetic field
• Entanglement entropy and nonabelian gauge symmetry
• Aspects of Entanglement Entropy for Gauge Theories
• Distributional Geometry of Squashed Cones
• Entanglement Entropy of Gapped Phases and Topological Order in Three dimensions
• The entanglement of distillation for gauge theories
• Entanglement entropy for a Maxwell field: Numerical calculation on a two dimensional lattice
• Entanglement entropy of a Maxwell field on the sphere
• Entanglement entropy for even spheres
• Entanglement Entropy of U(1) Quantum Spin Liquids
• Notes on Entanglement in Abelian Gauge Theories
• Entanglement in Weakly Coupled Lattice Gauge Theories
• A note on electromagnetic edge modes

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