  We study holographically non-local observables in field theories at finite
temperature and in the large $d$ limit. These include the Wilson loop, the
entanglement entropy, as well as an extension to various dual extremal surfaces
of arbitrary codimension. The large $d$ limit creates a localized potential in
the near horizon regime resulting in a simplification of the analysis for the
non-local observables, while at the same time retaining their qualitative
physical properties. Moreover, we study the monotonicity of the coefficient
$\alpha$ of the entanglement's area term, the so called area theorem. We find
that the difference between the UV and IR of the $\alpha$-values, normalized
with the thermal entropy, converges at large $d$ to a constant value which is
obtained analytically. Therefore, the large $d$ limit may be used as tool for
the study and (in)validation of the renormalization group monotonicity
theorems. All the expectation values of the observables under study show rapid
convergence to certain values as $d$ increases. The extrapolation of the large
$d$ limit to low and intermediate dimensions shows good quantitative agreement
with the numerical analysis of the observables.
