Entanglement Entropy and Duality in AdS(4)

TL;DR

This paper investigates how small changes in entanglement entropy relate to the modular Hamiltonian in AdS(4), revealing a duality and conditions for thermodynamic consistency using holographic methods.

Contribution

It computes holographic variations of entanglement entropy and modular Hamiltonian for circular curves in AdS(4), uncovering a duality and conditions for the first law of thermodynamics.

Findings

Agreement with the first law requires constant entangling curve line element

Discovery of electric-magnetic duality in entanglement measures

Holographic energy-momentum/Cotton tensor duality manifestation

Abstract

Small variations of the entanglement entropy \delta S and the expectation value of the modular Hamiltonian \delta E 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, \delta S = \delta E, 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.