A note on the extensivity of the holographic entanglement entropy

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.Comment: 12 pages and 2 figures; one reference added; Significant additions to section 3, involving new results and a more pedagogical presentatio