On-Shell Action for Type IIB Supergravity and Superstrings on $AdS_5 \times S^5$

AdS/CFT predicts that the value of the on-shell action for type IIB Supergravity (SUGRA) on $AdS_5 \times S^5$ background must be a non-zero number completely determined from the boundary theory. We examine this statement within Sen's formalism for type IIB SUGRA and find that consistency with AdS/CFT requires us to add a specific boundary term to the action. We contrast our resolution with two other resolutions recently proposed in the literature in the context of different approaches to type IIB SUGRA. We explain how our resolution presents a strong benchmark for the possible boundary term of the complete spacetime action for type IIB superstring and how it may possibly lead to a piece of evidence for the strongest form of AdS/CFT conjecture in $AdS_5 \times S^5$. We also comment on the fate of the on-shell action for general self-dual $p$-form fields in Sen's formalism in any curved backgrounds.