Corrections to holographic entanglement plateau

Abstract

We investigate the robustness of the Araki-Lieb inequality in a two-dimensional (2D) conformal field theory (CFT) on torus. The inequality requires that ΔS = S(L) − |S(L − ℓ) − S(ℓ)| is nonnegative, where S(L) is the thermal entropy and S(L − ℓ), S(ℓ) are the entanglement entropies. Holographically there is an entanglement plateau in the BTZ black hole background, which means that there exists a critical length such that when ℓ ≤ ℓc the inequality saturates ΔS =0. In thermal AdS background, the holographic entanglement entropy leads to ΔS = 0 for arbitrary ℓ. We compute the next-to-leading order contributions to ΔS in the large central charge CFT at both high and low temperatures. In both cases we show that ΔS is strictly positive except for ℓ = 0 or ℓ = L. This turns out to be true for any 2D CFT. In calculating the single interval entanglement entropy in a thermal state, we develop new techniques to simplify the computation. At a high temperature, we ignore the finite size correction such that the problem is related to the entanglement entropy of double intervals on a complex plane. As a result, we show that the leading contribution from a primary module takes a universal form. At a low temperature, we show that the leading thermal correction to the entanglement entropy from a primary module does not take a universal form, depending on the details of the theory.