On minimal entanglement wedge cross section for holographic entanglement negativity
arXiv:2002.10272 · doi:10.3390/universe10030125
Abstract
We demonstrate the equivalence of two different conjectures in the literature for the holographic entanglement negativity in AdS/CFT, modulo certain constants. These proposals involve certain algebraic sums of bulk geodesics homologous to specific combinations of subsystems, and the entanglement wedge cross section (EWCS) backreacted by a cosmic brane for the conical defect geometry in the bulk gravitational path integral. It is observed that the former conjectures reproduce the field theory replica technique results in the large central charge limit whereas the latter involves constants related to the Markov gap. In this context we establish an alternative construction for the EWCS of a single interval in a CFT at a finite temperature to resolve an issue for the latter proposal involving the thermal entropy elimination for the holographic entanglement negativity. Our construction for the EWCS correctly reproduces the corresponding field theory results modulo the Markov gap constant in the large central charge limit.
28 pages, 5 figures, 3 appendices, v3: matches the published version
References in corpus (13)
- Towards a derivation of holographic entanglement entropy
- Entanglement negativity in quantum field theory
- Causality & holographic entanglement entropy
- Entanglement entropy of two disjoint intervals in conformal field theory II
- Deriving covariant holographic entanglement
- Finite temperature entanglement negativity in conformal field theory
- Comments on Entanglement Negativity in Holographic Field Theories
- Conformal Blocks and Negativity at Large Central Charge
- Replica wormholes and capacity of entanglement
- Holographic entanglement negativity and replica symmetry breaking
- Multipartite Reflected Entropy
- Islands for Entanglement Negativity
- The Markov gap for geometric reflected entropy