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2014

Topological aspects of generalized gravitational entropy

Haehl, Felix M., Hartman, Thomas, Marolf, Donald et al.

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The holographic prescription for computing entanglement entropy requires that the bulk extremal surface, whose area encodes the amount of entanglement, satisfies a homology constraint.

Usually this is stated as the requirement of a (spacelike) interpolating surface that connects the region of interest and the extremal surface.
We investigate to what extent this constraint is upheld by the generalized gravitational entropy argument, which relies on constructing replica symmetric q-fold covering spaces of the bulk, branched at the extremal surface.
We prove (at the level of topology) that the putative extremal surface satisfies the homology constraint if and only if the corresponding branched cover can be constructed for every positive integer q.

Topological aspects of generalized gravitational entropy · Around

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