1305.1064 (Javier Molina-Vilaplana)

On the Mutual Information between disconnected regions in AdS/CFT    [PDF]

Javier Molina-Vilaplana

In this note, we compute the holographic mutual information between two separated circular regions in a 3+1 dimensional gauge theory dual to AdS$_5 \times S^5$ through the AdS/CFT correspondence, in the limit in which the separation $L$ between the regions is much larger than their sizes $a$. Our calculation uses some previous results concerning the holographic computation of the long distance correlator of two distant Wilson loops. We show that in these regimes, the holographic mutual information follows a power law decaying behaviour proportional to $\sqrt{\lambda}$ with $\lambda$ the t'Hooft coupling of the gauge theory. This result contradicts a conjectured sharp vanishing of the holographic mutual information between disjoint regions for the large separation regime and has been also compared with a recent result concerning a 3+1 dimensional free CFT.

View original: http://arxiv.org/abs/1305.1064