R^2 Corrections for 5D Black Holes and Rings
Monica Guica, Lisa Huang, Wei Li, Andrew Strominger
TL;DR
The paper addresses the problem of understanding leading entropy corrections in five-dimensional BPS black holes and rings arising from higher-derivative terms, focusing on $R^2$ corrections descended from M-theory reductions. It adopts Wald's entropy formalism in 5D to derive the corrections and applies them to the supersymmetric black ring and the BMPV black hole, then compares the macroscopic results to microscopic expectations from 4D compactifications and topological string theory. The main contributions are the explicit macroscopic corrections: $\Delta S_{BR} = \frac{\pi}{6} (c_2 \cdot p) \sqrt{\hat{q}_0 / D}$ for the black ring, and a derived expression for $\Delta S_{BMPV}$ in terms of horizon moduli $Y^A$ and charges, along with a discussion of how these corrections align with, or differ from, 4D predictions through the 4D-5D relation. The findings show a precise match at leading order for the black ring between macroscopic $R^2$ corrections and the leading microscopic corrections, while for BMPV the correspondence is partial and the 5D corrections exhibit subleading mismatches with the 4D/topological string expectations, underscoring the still-limited understanding of 5D F-terms and the need for a more complete 5D macro/micro framework.
Abstract
We study higher-order corrections to two BPS solutions of 5D supergravity, namely the supersymmetric black ring and the spinning black hole. Due in part to our current relatively limited understanding of F-type terms in 5D supergravity, the nature of these corrections is less clear than that of their 4D cousins. Effects of certain $R^2$ terms found in Calabi-Yau compactification of M-theory are specifically considered. For the case of the black ring, for which the microscopic origin of the entropy is generally known, the corresponding higher order macroscopic correction to the entropy is found to match a microscopic correction, while for the spinning black hole the corrections are partially matched to those of a 4D $D0-D2-D6$ black hole.