A note on the extensivity of the holographic entanglement entropy

TL;DR

This paper investigates conditions under which holographic entanglement entropy exhibits extensive behavior, especially in the context of conformal field theories in 2+1 dimensions with external fields, extending known results to zero temperature.

Contribution

It demonstrates that holographic entanglement entropy remains extensive at zero temperature for certain 2+1D conformal field theories with magnetic and electric condensates.

Findings

Extensivity occurs in geometries capped in the infrared region.

Extensivity persists at zero temperature for specific 2+1D CFTs with condensates.

Holographic ansatz predicts volume-law entanglement in these cases.

Abstract

We consider situations where the renormalized geometric entropy, as defined by the AdS/CFT ansatz of Ryu and Takayanagi, shows extensive behavior in the volume of the entangled region. In general, any holographic geometry that is `capped' in the infrared region is a candidate for extensivity provided the growth of minimal surfaces saturates at the capping region, and the induced metric at the `cap' is non-degenerate. Extensivity is well-known to occur for highly thermalized states. In this note, we show that the holographic ansatz predicts the persistence of the extensivity down to vanishing temperature, for the particular case of conformal field theories in 2+1 dimensions with a magnetic field and/or electric charge condensates.