Holographic entanglement negativity conjecture for adjacent intervals in $AdS_3/CFT_2$

Understand

We propose a holographic entanglement negativity conjecture involving the bulk geometry, for mixed states of adjacent intervals in $(1+1)$-dimensional dual conformal field theories through the $AdS/CFT$ correspondence.

• The holographic entanglement negativity is obtained from a specific algebraic sum of the geodesics anchored on respective intervals on the boundary which reduces to the holographic mutual information between them.
• Utilizing our conjecture we obtain the entanglement negativity of adjacent intervals in zero and finite temperature ($1+1$)-dimensional holographic conformal field theories dual to the bulk $AdS_3$ vacuum and the Euclidean BTZ black hole respectively.
• Our holographic conjecture exactly reproduces the conformal field theory results obtained through the replica technique, in the large central charge limit.