On minimal entanglement wedge cross section for holographic entanglement negativity

TL;DR

This paper proves the equivalence of two conjectures for holographic entanglement negativity in AdS3/CFT2, providing an alternative construction for the entanglement wedge cross section that aligns with field theory results at large central charge.

Contribution

It establishes the equivalence of different holographic negativity conjectures and introduces a new construction for the entanglement wedge cross section at finite temperature.

Findings

Conjectures reproduce field theory results in the large central charge limit.

The alternative construction resolves issues related to thermal entropy elimination.

The approach aligns with the Markov gap constant in the large central charge limit.

Abstract

We demonstrate the equivalence of two different conjectures in the literature for the holographic entanglement negativity in AdS$_3$/CFT$_2$, 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$_2$ 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.