Non-local observables at finite temperature in AdS/CFT

Abstract

Within gauge/gravity duality, we consider the AdS-Schwarzschild metric in arbitrary dimensions. We obtain analytical closed-form results for the two-point function, Wilson loop and entanglement entropy for strip geometries in the finite-temperature fieldtheory dual. According to the duality, these are given by the area of minimal surfaces of different dimension in the gravity background. Our analytical results involve generalised hypergeometric functions. We show that they reproduce known numerical results to great accuracy. Our results allow to identify new physical behaviour: for instance, we consider the entanglement density, i.e. the difference of entanglement entropies at finite and vanishing temperature divided by the volume of the entangling region. For field theories of dimension seven or higher, we find that the entanglement density displays non-monotonic behaviour as function of · T , with the strip width and T the temperature. This implies that the area theorem, proven for RG flows in general dimensions, does not apply here. This may signal the emergence of new degrees of freedom for AdS Schwarzschild black holes in eight or more dimensions.

Holographic anisotropic background with confinement-deconfinement phase transition

“…(compare with [88,89]). The advantage of dealing with the HEE density is that it has no divergences.…”

“…This enhancement depends on geometrical (length), and thermodynamical (temperature T and chemical potential µ) parameters. The HEE density [86][87][88][89] is a more convenient object for study since it does not suffer from ultraviolet divergencies. The HEE and its density undergo jumps and these jumps increase while increasing angle.…”

An inverse mass expansion for the mutual information in free scalar QFT at finite temperature

“…[15]). Most of these focus mainly on the geometry of the BTZ black hole [16][17][18][19], which is also relevant to two-dimensional CFTs, as this is the only black hole geometry where minimal surfaces can be expressed analytically. Entanglement in harmonic lattice systems at finite temperature has been studied in [20].…”

Saturation of the quantum null energy condition in far-from-equilibrium systems

“…Preliminaries-HEE for the AdS d Schwarzschild black brane was considered by Fischler and Kundu who gave infinite series representations in terms of ratios of Γ-functions [42] and more recently by Erdmenger and Miekley [43] who expressed their results in closed form in terms of Meijer G-functions. For QNEC, it is necessary to compute nonequal time HEE, which is not straightforward using these methods.…”

“…The first line recovers the HEE results of [42,43]. The second derivative of the area (A17) with respect to AEλ evaluated at λ ¼ 0 yields the QNEC quantity S 00 AE used in the main text:…”