  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.
