Higher-Derivative Supergravity, AdS$_4$ Holography, and Black Holes

Understand

We use conformal supergravity techniques to study four-derivative corrections in four-dimensional gauged supergravity.

• We show that the four-derivative Lagrangian for the propagating degrees of freedom of the $\mathcal{N}=2$ gravity multiplet is determined by two real dimensionless constants.
• We demonstrate that all solutions of the two-derivative equations of motion in the supergravity theory also solve the four-derivative equations of motion.
• These results are then applied to explicitly calculate the regularized on-shell action for any asymptotically locally AdS$_4$ solution of the two-derivative equations of motion.