The dark (BPS) side of thermodynamics in Minkowski4

Abstract

We explore the BPS limit of asymptotically flat black hole thermodynamics, drawing analogies with recent studies of black holes in anti-de Sitter space. Although ultimately motivated by supersymmetry and quantum gravity, the BPS limit is classically well-defined for the dyonic Kerr-Newman black holes in pure Einstein-Maxwell theory and various generalizations with additional scalars and gauge fields that admit embedding in $$ \mathcal{N} $$ N = 2 supergravity (for concreteness we consider the STU model). This limit is manifestly different from extremality as it includes a family of rotating Euclidean saddles that represent a (fictitious) thermal branch, smoothly connected with the extremal static Reissner-Nordström black hole and its generalizations with extra matter. We are able to evaluate unambiguously all BPS chemical potentials, finding constant imaginary angular velocity as a consequence of Wick rotation. In the mixed ensemble of fixed magnetic and varying electric charges, we derive the OSV formula that is crucial for the microscopic understanding of the system, and provide evidence that it should be interpreted as a fixed-point formula.

Higher-derivative corrections to flavoured BPS black hole thermodynamics and holography

“…Supersymmetric non-extremal sections of black hole solutions, of the type first discussed in [1] for the asymptotically AdS case, have recently proven useful also in the context of microstate counting for asymptotically flat solutions in four [89][90][91][92] and five [93] dimensions, where they are interpreted as Euclidean saddles of the gravitational path integral computing a string theory supersymmetric index. The role of higher-derivative corrections in this context has been emphasized very recently in [94,95].…”

Maximally symmetric nuts in 4d 𝒩 = 2 higher derivative supergravity

“…In fact single centered black holes in Minkowski are already known to obey (4.1) with their corresponding gluing rule, see [1], from a series of previous works, [51][52][53], which served as an inspiration for the general conjecture in first place. It is important here to make the following remark: it was shown in [54] via BPS thermodynamics that asymptotically flat single centered black holes do indeed correspond to ω = −1 (in the conventions of (4.1)), such that the potential T-tower of corrections vanishes. However, it would be misleading to expect that potentially new asymptotically flat examples with ω = −1 might lead to non-vanishing T-corrections, as this is not possible.…”

“…11 Since we only rely on Euclidean supersymmetry, we do not distinguish here between spaces that correspond (upon Wick rotation) to Lorentzian black holes and Euclidean black saddles discussed in 4d in [20,13,38]. These are indeed topologically indistinguishable in equivariant localization and produce the same off-shell results.…”

“…Note also that the above gluing rules are naturally adapted from the two derivative description of asymptotically AdS black holes, as in[35], with electric gauging parameters g I . Depending on the frame, in which the prepotential is defined, there could be an additional sign in the gluing rules that becomes manifest in the ungauged limit, see[38]. This technical detail is more naturally addressed at the level of the complete internal geometry inside string theory,[58].…”