Speaker
Description
In the AdS/CFT correspondence, holographic observables such as the free energy are typically compared with the Euclidean on-shell action of lower-dimensional gauged supergravity. From a first-principles perspective, however, these quantities should arise directly from the ten-dimensional Type IIB supergravity on-shell action in the leading order. A longstanding puzzle is that the Type IIB pseudo-action evaluated on the $AdS_5 \times S^5$ solution vanishes, apparently
obstructing a direct holographic derivation. A recent proposal by Kurlyand and Tseytlin resolves this issue within the Pasti--Sorokin--Tonin (PST) formulation of Type IIB supergravity by
introducing an additional topological boundary term, yielding a non-vanishing on-shell action consistent with the holographic result.
This construction, however, was originally established only for a restricted class of backgrounds, notably the $AdS_5 \times S^5$
solution with vanishing two-form fields. In this talk, I revisit and extend this framework to a broader class of Type IIB backgrounds relevant for holography. In particular, I analyze geometries of the form $AdS_5 \times M_5$, including both the canonical $S^5$ compactification and deformed solutions such as the Lunin--Maldacena
background, as well as more general configurations of the type $AdS_4 \times M_6$. By introducing a generalized topological correction to the ten-dimensional action under milder assumptions, allowing, in particular, for non-vanishing two-form potentials, I demonstrate that the resulting ten-dimensional on-shell actions precisely reproduce the corresponding lower-dimensional gauged supergravity results.