An operator product expansion for the mutual information in AdS/CFT

We investigate the behavior of the mutual information I-AB between two "small" and wide separated spherical regions A and B in the N = 4 SYM gauge theory dual to Type JIB string theory in AdS(5) x S-5. To this end, the mutual information is recasted in terms of correlators of surface operators W(Sigma) defined along a surface Sigma within the boundary gauge theory. This construction relies on the strong analogies between the twist-field operators appearing in the replica trick method used for the computation of the entanglement entropy, and the disorder-like surface operators in gauge theories. In the AdS/CFT correspondence, a surface operator W(Sigma) corresponds to having a D3-brane in AdS(5) x S-5 ending on the boundary along the prescribed surface Sigma. Then, a long distance expansion for I-AB is provided. The coefficients of the expansion appear as a byproduct of the operator product expansion for the correlators of the operators W(Sigma) with the chiral primaries of the theory. We find that, while undergoing a phase transition at a critical distance, the holographic mutual information, instead of strictly vanishing, decays with a power law whose leading contributions of order O(N-0), originate from the exchange of pairs of the lightest bulk particles between A and B. These particles correspond to operators in the boundary field theory with the smallest scaling dimensions. (C) 2014 The Author. Published by Elsevier B.V.