Calibrated Entanglement Entropy

TL;DR

This paper introduces a calibration-based approach to compute holographic entanglement entropy in 3D gravity and warped AdS3 geometries, unifying minimal surface determination through special Lagrangian cycles.

Contribution

It demonstrates that calibrations can systematically identify minimal surfaces for entanglement entropy in holography, extending to warped geometries and higher dimensions.

Findings

Calibration method unifies minimal surface calculations

Applicable to warped AdS3 geometries

Potential generalizations to higher dimensions

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.