Abstract
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 mathcal{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 mathcal{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 \U0001d54e 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 \U0001d54b tower. Backgrounds preserving less supersymmetry, such as the under-rotating black holes in flat space, the holographic squashed S3, and the static/rotating twisted and non-twisted Kerr-Newman-like black holes in AdS4 lead to a more general refined version of the corresponding gravitational blocks as dictated by the supersymmetric gluing rules.
Highlights
Fixed points of their canonical isometry, and as a limiting case a large set of backgrounds with fixed two-submanifolds
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
The conjecture is shown to be in agreement with a number of available results for different BPS backgrounds with both Minkowski and AdS asymptotics. 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
Summary
Since ω is conjugate to the angular momentum, this is the static limit of the under-rotating non-BPS black holes in flat space and the general rotating black holes with a twist in AdS4, to be discussed in sections 3.2 and 4.3 respectively At two derivatives the latter solutions are well-understood holographically via a dual field theory localization calculation, see [37, 38, 46] and references thereof. The minimal/universal limit, nV = 0: the case of minimal supergravity with no additional vector multiplets allows for arbitrary ω but is very special since one only has the single section X0 and corresponding Coulomb branch parameter χ0 This limit is important in all asymptotically AdS4 examples since holographically it captures a universal sector of all dual three-dimensional field theories, as stressed in [49, 50]. In this sense we have just listed the five pillars on which the general conjecture gets its support, in addition to the well-established two-derivative foundation in [10]
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