Article

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

Journal ar
Nuclear Physics B
  • Volumen: 888
  • Fecha: 16 September 2014
  • Páginas: 1-16
  • ISSN: 05503213
  • Source Type: Journal
  • DOI: 10.1016/j.nuclphysb.2014.09.005
  • Document Type: Article
  • Publisher: Elsevier
© 2014 The Author.We investigate the behavior of the mutual information IAB between two "small" and wide separated spherical regions A and B in the N=4 SYM gauge theory dual to Type IIB string theory in AdS5×S5. To this end, the mutual information is recasted in terms of correlators of surface operators W(¿) defined along a surface ¿ 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(¿) corresponds to having a D3-brane in AdS5×S5 ending on the boundary along the prescribed surface ¿. Then, a long distance expansion for IAB is provided. The coefficients of the expansion appear as a byproduct of the operator product expansion for the correlators of the operators W(¿) 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(N0), 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.

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