Higher-Derivative Supergravity, Wrapped M5-branes, and Theories of Class $\mathcal{R}$

We study the interplay between four-derivative 4d gauged supergravity, holography, wrapped M5-branes, and theories of class $\mathcal{R}$. Using results from Chern-Simons theory on hyperbolic three-manifolds and the 3d-3d correspondence we are able to constrain the two independent coefficients in the four-derivative supergravity Lagrangian. This in turn allows us to calculate the subleading terms in the large-$N$ expansion of supersymmetric partition functions for an infinite class of three-dimensional $\mathcal{N}=2$ SCFTs of class $\mathcal{R}$. We also determine the leading correction to the Bekenstein-Hawking entropy of asymptotically AdS$_4$ black holes arising from wrapped M5-branes. In addition, we propose and test some conjectures about the perturbative partition function of Chern-Simons theory with complexified ADE gauge groups on closed hyperbolic three-manifolds.