One-loop quantum holography for higher dimensional black holes

The one-loop quantum corrections to the free energy associated with scalar field in a higher dimensional static curved space-time is investigated making use of the conformal transformation method. For a space-time with bifurcate horizon, horizon divergences are accounted for choosing the Planck length as natural cutoff. The leading term in the high temperature quantum correction satisfies holographically the “area law”, like the tree level Bekenstein-Hawking term. Furthermore it is stressed that only for the asymptotically AdS black holes one may have a microscopic interpretation of the entropy also at quantum level.