  We study the renormalization of Entanglement Entropy in holographic CFTs dual
to Lovelock gravity. It is known that the holographic EE in Lovelock gravity is
given by the Jacobson-Myers (JM) functional. As usual, due to the divergent
Weyl factor in the Fefferman-Graham expansion of the boundary metric for
Asymptotically AdS spaces, this entropy functional is infinite. By considering
the Kounterterm renormalization procedure, which utilizes extrinsic boundary
counterterms in order to renormalize the on-shell Lovelock gravity action for
AAdS spacetimes, we propose a new renormalization prescription for the
Jacobson-Myers functional. We then explicitly show the cancellation of
divergences in the EE up to next-to-leading order in the holographic radial
coordinate, for the case of spherical entangling surfaces. Using this new
renormalization prescription, we directly find the $C-$function candidates for
odd and even dimensional CFTs dual to Lovelock gravity. Our results illustrate
the notable improvement that the Kounterterm method affords over other
approaches, as it is non-perturbative and does not require that the Lovelock
theory has limiting Einstein behavior.
