Entanglement Entropy and Duality in AdS(4)
arXiv:1503.00627 · doi:10.1016/j.nuclphysb.2015.04.027
Abstract
Small variations of the entanglement entropy δS and the expectation value of the modular Hamiltonian δE are computed holographically for circular entangling curves in the boundary of AdS(4), using gravitational perturbations with general boundary conditions in spherical coordinates. Agreement with the first law of thermodynamics, δS = δE, requires that the line element of the entangling curve remains constant. In this context, we also find a manifestation of electric-magnetic duality for the entanglement entropy and the corresponding modular Hamiltonian, following from the holographic energy-momentum/Cotton tensor duality.
43 pages, 2 figures, v2: a few clarifications have been added; final version to appear in Nucl. Phys. B
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