Geometric entropy and edge modes of the electromagnetic field

By William Donnelly, Aron C. Wall. 2015

164 citations recorded by the source corpus.

We calculate the vacuum entanglement entropy of Maxwell theory in a class of curved spacetimes by Kaluza-Klein reduction of the theory onto a two-dimensional base manifold. Using two-dimensional duality, we express the geometric entropy of the electromagnetic field as the entropy of a tower of scalar fields, constant electric and magnetic fluxes, and a contact term, whose leading-order divergence was discovered by Kabat. The complete contact term takes the form of one negative scalar degree of freedom confined to the entangling surface. We show that the geometric entropy agrees with a statistical definition of entanglement entropy that includes edge modes: classical solutions determined by their boundary values on the entangling surface. This resolves a long-standing puzzle about the statistical interpretation of the contact term in the entanglement entropy. We discuss the implications of this negative term for black hole thermodynamics and the renormalization of Newton's constant.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1505c3b2d1a1f248b52704377d61708c2a3caaf2

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Citations in the corpus

Quantum extremal islands made easy. Part I. Entanglement on the brane (2020, background): “With the connection between the renormalization of Newton’s constant and the area law contribution in entanglement entropy [138, 141], this negative renormalization generates a puzzle which, however, was finally resolved in terms of edge modes in [142, 143].”
Entropy, extremality, euclidean variations, and the equations of motion (2017, methodology): “This integration is often referred to as summing over edge modes [39, 40], there they write the partition in a smooth black hole background for abelian gauge fields in terms of the partition function in a brick wall geometry summed over all possible electric fluxes across the boundary.”
Relative entropy equals bulk relative entropy (2015, background): “Recently, [18, 19] carried out explicitly the field theory calculation, being careful with the center variables.”
The Ryu–Takayanagi Formula from Quantum Error Correction (2016, background): “Indeed in [42,43] it was explained how correctly including this central contribution to the entropy from the electric fluxes through the entangling surface resolves an old discrepancy [68] between replica-trick and direct Hilbert space calculations of the entropy of a region inMaxwell theory.”
Entanglement entropy: Holography and renormalization group (2018, background): “…and attempts to define entanglement entropy in gauge theories, see e.g. (Aoki et al., 2015; Casini et al., 2014; Chen et al., 2015; Donnelly, 2014; Donnelly and Wall, 2015, 2016; Ghosh et al., 2015; Hung and Wan, 2015; Ma, 2016; Pretko and Senthil, 2016; Radicevic, 2014, 2016; Soni and Trivedi,…”
Local subsystems in gauge theory and gravity (2016, methodology): “In abelian gauge theory, the surface charges are needed to provide agreement with Euclidean methods, and to obtain agreement between the conformal anomaly and the universal logarithmic term in the entanglement entropy [24, 25].”