Covariant holographic entanglement negativity for disjoint intervals in $$AdS_3/CFT_2$$

Abstract

We advance a construction for the covariant holographic entanglement negativity for time dependent mixed states of disjoint intervals in (1 + 1) dimensional conformal field theories (C FT 1+1) dual to bulk non static Ad S 3 geometries. Application of our proposal to such mixed states in a C FT 1+1 dual to bulk non extremal and extremal rotating BTZ black holes exactly reproduces the replica technique results in the large central charge limit. We also investigate the time dependent holographic entanglement negativity for such mixed states in a C FT 1+1 dual to a bulk Vaidya-Ad S 3 geometry in the context of their thermalization involving bulk black hole formation.

Page curve for entanglement negativity through geometric evaporation

“…In a recent article [53], the authors computed the gravitational path integral corresponding to the Renyi negativities in holographic theories and demonstrated that it is dominated by a bulk replica symmetry breaking saddle. Following this in [48], the authors of the present article demonstrated that for two dimensional holographic C F T s and for the case of subsystems involving spherical entangling surfaces in higher dimensions, the computation in [53] also serves as a proof of the holographic proposals [40,43,45].…”

“…We then briefly describe the entanglement negativity of a bipartite system in a random mixed state and the corresponding Page curve derived using the random matrix techniques in [70]. Subsequently, we discuss the holographic entanglement negativity proposal for various mixed state configurations in the AdS 3 /CFT 2 scenario conjectured in [40,43,45].…”

“…Furthermore, this led to the first attempt for the holographic entanglement negativity of pure states made in [39]. Soon after another distinct holographic conjecture involving the algebraic sum of the areas of the extremal surfaces for various pure and mixed state configurations of the adjacent, the disjoint and the single intervals in a zero and finite temperature C F T 1+1 was proposed in a series of articles [40][41][42][43][44][45][46][47]. Recently, this proposal was re-expressed in terms of the areas of the combination of backreacting cosmic branes corresponding to Renyi entropy of order half [48].…”

“…Apart from the above mentioned proposals another alternative holographic construction for the entanglement negativity involving the backreacting entanglement wedge cross section (EWCS) or the Reflected entropy of order half was developed in [49,50]. Note that the results from the holographic proposals involving the algebraic sum of the areas of the extremal surfaces [40,43,45], precisely match with the corresponding results obtained using the EWCS in [49][50][51][52]. In a recent article [53], the authors computed the gravitational path integral corresponding to the Renyi negativities in holographic theories and demonstrated that it is dominated by a bulk replica symmetry breaking saddle.…”

“…In section 2 we review the model involving the partial dimensional reduction described in [20] to obtain the Page curve for the entanglement entropy of the entire bath/radiation coupled to a JT black hole. Following this we briefly review [70] where the authors obtain the entanglement negativity of a random bipartite mixed state and then go on to describe the holographic entanglement negativity construction proposed in [43,45]. In section 3 we describe our computation of the entanglement negativity of the pure and mixed state configurations involving disjoint, adjacent and single intervals in a bath C F T 2 coupled to an evaporating non-extremal JT gravity obtained through the partial dimensional reduction of the BTZ black hole.…”