Holographic entanglement entropy from minimal surfaces with/without extrinsic curvature

TL;DR

This paper explores additional minimal surfaces with extrinsic curvature for holographic entanglement entropy, using regularization techniques to identify the true minimal surface among various candidates.

Contribution

It introduces the existence of minimal surfaces with non-zero extrinsic curvature and provides a method to determine the correct surface for entanglement entropy calculations.

Findings

Identification of new minimal surfaces with extrinsic curvature

Regularization method for curvature invariants on manifolds with squashed cones

Guidelines to select the true minimal surface for holographic entanglement entropy

Abstract

In this paper we show that in addition to the known minimal surfaces which appear in the literature for computing the entanglement entropy there are other minimal surfaces with non-zero extrinsic curvature. We use the approach of regularization procedure for computing the quadratic and cubic curvature invariants on manifolds with squashed cones. The results can be used to find the leading and universal terms of the holographic entanglement entropy to understand which solution corresponds to the actual minimal surface.