  We revisit the construction in four-dimensional gauged $Spin(4)$ supergravity
of the holographic duals to topologically twisted three-dimensional
$\mathcal{N}=4$ field theories. Our focus in this paper is to highlight some
subtleties related to preserving supersymmetry in AdS/CFT, namely the inclusion
of finite counterterms and the necessity of a Legendre transformation to find
the dual to the field theory generating functional. Studying the geometry of
these supergravity solutions, we conclude that the gravitational free energy is
indeed independent from the metric of the boundary, and it vanishes for any
smooth solution.
