Holographic Origin of a Maximization and Higher-Derivative AdS_{5}/CFT_{4}

We develop a consistent partially off-shell framework for evaluating higher-derivative actions of five-dimensional N=1 gauged supergravity with Abelian vector multiplets on AdS_{5}. Using the superconformal formalism, we show that the resulting holographic expression reproduces the trial a-anomaly coefficient of the dual conformal field theory, identifying the supergravity equations of motion with a maximization. We present an exact correspondence between Chern-Simons couplings and the anomaly polynomial of the boundary theory. We illustrate our proposal by applying it to all known two- and four-derivative actions, including the "off-diagonal" invariants never before considered in the gauged supergravity literature. Finally, we argue that all invariants beyond four derivative yield no genuinely new contributions to asymptotically AdS_{5} BPS backgrounds, but instead reduce to linear combinations of the established two- and four-derivative actions.