Calibrated Entanglement Entropy

Abstract

The Ryu-Takayanagi prescription reduces the problem of calculating entanglement entropy in CFTs to the determination of minimal surfaces in a dual anti-de Sitter geometry. For 3D gravity theories and BTZ black holes, we identify the minimal surfaces as special Lagrangian cycles calibrated by the real part of the holomorphic one-form of a spacelike hypersurface. We show that (generalised) calibrations provide a unified way to determine holographic entanglement entropy from minimal surfaces, which is applicable to warped AdS${}_3$ geometries. We briefly discuss generalisations to higher dimensions.

v1 22 pages, 1 figure; v2 appendix improved and moved into the body to show the application of calibrations to find minimal surfaces in warped AdS, matches published version

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