The Unreasonable Effectiveness of Higher-Derivative Supergravity in AdS$_4$ Holography

We study four-derivative corrections to four-dimensional $\mathcal{N}=2$ minimal gauged supergravity and show that they are controlled by two real constants. The solutions of the equations of motion in the two-derivative theory are not modified by the higher-derivative corrections. We use this to derive a general formula for the regularized on-shell action for any asymptotically locally AdS$_4$ solution of the theory and show how the higher-derivative corrections affect black hole thermodynamic quantities in a universal way. We employ our results in the context of holography to derive explicit expressions for the subleading corrections in the large $N$ expansion of supersymmetric partition functions on various compact manifolds for a large class of three-dimensional SCFTs.