Exploring the relation between 4D and 5D BPS solutions
Klaus Behrndt, Gabriel Lopes Cardoso, Swapna Mahapatra
TL;DR
The paper develops a precise 4D/5D correspondence for BPS solutions in N=2 supergravity with cubic prepotentials, showing that stationary solutions in both dimensions are fixed by the same harmonic functions and attractor equations, and provides an explicit dictionary linking 4D stabilisation data to 5D solutions. Through examples like black holes and black rings in Gödel-Taub-NUT spacetimes, it demonstrates that 4D and 5D entropies agree and that the dictionary extends to more general prepotentials. It then examines how R^2-corrections affect the 4D–5D connection, illustrating that higher-derivative terms can cloak singularities and yield Wald-type entropy corrections that are consistent across dimensions. The results offer a robust framework for translating higher-derivative corrections between 4D and 5D BPS solutions and for understanding their physical implications in Taub-NUT geometries.
Abstract
Based on recent proposals linking four and five-dimensional BPS solutions, we discuss the explicit dictionary between general stationary 4D and 5D supersymmetric solutions in N=2 supergravity theories with cubic prepotentials. All these solutions are completely determined in terms of the same set of harmonic functions and the same set of attractor equations. As an example, we discuss black holes and black rings in Gödel-Taub-NUT spacetime. Then we consider corrections to the 4D solutions associated with more general prepotentials and comment on analogous corrections on the 5D side.