Holographic entanglement negativity for disjoint intervals in $Ad{S}_3/CF{T}_2$

Abstract

We advance a holographic construction for the entanglement negativity of bipartite mixed state configurations of two disjoint intervals in $(1+1)$ dimensional conformal field theories ($CF{T}_{1+1}$) through the $Ad{S}_3/CF{T}_2$ correspondence. Our construction constitutes the large central charge analysis of the entanglement negativity for mixed states under consideration and involves a specific algebraic sum of bulk space like geodesics anchored on appropriate intervals in the dual $CF{T}_{1+1}$. The construction is utilized to compute the holographic entanglement negativity for such mixed states in $CF{T}_{1+1}$s dual to bulk pure $Ad{S}_3$ geometries and BTZ black holes respectively. Our analysis exactly reproduces the universal features of corresponding replica technique results in the large central charge limit which serves as a consistency check.

17 pages, 4 figures