Non-local observables at finite temperature in AdS/CFT

TL;DR

This paper derives analytical formulas for non-local observables like two-point functions, Wilson loops, and entanglement entropy at finite temperature in AdS/CFT, revealing new physical behaviors in higher dimensions.

Contribution

It provides the first analytical closed-form results for these observables in arbitrary dimensions at finite temperature within gauge/gravity duality.

Findings

Analytical results match numerical data accurately.

Entanglement density shows non-monotonic behavior in dimensions ≥7.

Area theorem does not hold in higher-dimensional cases.

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 field-theory 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 l*T, with l 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.