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Holographic Complexity for disentangled states
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In this paper we consider the maximal volume and the action, which are conjectured to be gravity duals of the complexity, in the black hole geometries with end of the world branes. These geometries are duals of boundary states in CFTs which have small real space entanglement. When we raise the black hole temperature while keeping the cutoff radius, black hole horizons or end of the world branes come in contact with the cutoff surface. In this limit, holographic entanglement entropy reduces to 0. We studied the behavior of the volume and the action. We found that the volume reduces to 0 in this limit. The behavior of the action depends on their regularization. We study the implication of these results to the reference state of the holographic complexity both in the complexity = volume or the complexity = action conjectures.
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Does Boundary Distinguish Complexities?
In BCFT, boundary complexity increments show the same divergent structure for volume, action, and path-integral measures in d>2, but in d=2 the action measure gives a finite constant instead of a logarithmic divergence.
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