We reinterpret the OSV formula for the on-shell action/entropy function of asymptotically flat BPS black holes as a fixed point formula that is formally equivalent to a recent gluing proposal for asymptotically AdS4 black holes. This prompts a conjecture that the complete perturbative answer for the most general gravitational building block of 4d N=2 supergravity at a single fixed point takes the form of a Nekrasov-like partition function with equivariant parameters related to the higher-derivative expansion of the prepotential. In turn this leads to a simple localization-like proposal for a set of supersymmetric partition functions in (UV completed) 4d N=2 supergravity theories. The conjecture is shown to be in agreement with a number of available results for different BPS backgrounds with both Minkowski and AdS asymptotics. In particular, it follows that the OSV formula comes from the unrefined limit of the general expression including only the so-called W tower of higher derivatives, while the on-shell action of pure (Euclidean) AdS4 with round S3 boundary comes from the NS limit that includes only the T tower.

In this talk I discuss some work in progress concerning higher-derivative (HD) terms in 4d supergravity. In particular we'll focus on the simplest case of 4-derivative terms appearing in minimal gauged supergravity. This choice minimizes the freedom in the HD terms to two arbitrary constants, which can be determined by a holographic match. This gives a prediction about the reduction of 11d HD terms on S^7. We then derive holographic predictions for the first subleading terms of various supersymmetric partition functions in their expansion of the gauge group rank, N. Additionally we are able to evaluate the on-shell action for non-BPS solutions in supergravity, allowing us to discuss black hole thermodynamics in the presence of HD terms. (To request the Zoom link send email with empty text and subject "talk" to alejandro.cabo_bizet@kcl.ac.uk)

The microscopic description of the 4 dimensional supersymmetric (or BPS) black holes in flat space has already been well understood via the AdS/CFT correspondence on the black hole horizon. In this talk I address the similar problem of finding the dual description for the static BPS black holes in AdS_4 embeddable in M-theory. The gravity picture of an interpolation between asymptotic AdS_4 and AdS_2xS^2 on the horizon can be understood as a renormalization group (RG) flow between a 3d and a 1d superconformal field theory. I discuss in some detail both the gravity and the field theory side, providing evidence for their match. At the end I present a proposal for the 1d CFT states that make up the black hole entropy.