In the prototypical AdS5/CFT4 correspondence, the free energy of \( \mathcal{N} \) = 4 SU(N) super Yang-Mills theory is commonly reproduced from the Euclidean on-shell action of five-dimensional gauged supergravity — a consistent truncation of Type IIB supergravity — rather than computed directly in ten dimensions. A longstanding obstacle to the latter is that the conventional Type IIB pseudo-action evaluated on the AdS5 × S5 background vanishes identically, apparently precluding a first-principles holographic comparison. A recent proposal by Kurlyand and Tseytlin, based on the Pasti-Sorokin-Tonin formulation, resolves this issue for a special class of backgrounds including the AdS5 × S5 vacuum by introducing a topological term required for consistency, yielding a non-vanishing on-shell value in agreement with holography. In this work we extend this refinement to a broader class of Type IIB backgrounds by introducing a generalized topological correction under milder conditions, encompassing AdS geometries of generic dimension and non-vanishing 2-form potentials. We test the proposal on non-trivial solutions such as the Lunin-Maldacena background and the AdS4 S-fold solution, and find agreement with the corresponding lower-dimensional gauged supergravity on-shell actions and thereby with the expected holographic observables. Our results place direct holographic comparisons within the ten-dimensional Type IIB framework on firmer ground.
