String Theory Effects on Five-Dimensional Black Hole Physics

TL;DR

This work develops and analyzes five-dimensional N=2 supergravity with leading four-derivative (R^2) corrections, derived from M-theory on Calabi–Yau threefolds and organized through an off-shell conformal supergravity formalism. It constructs a broad class of BPS solutions—black holes, black strings, and black rings—via harmonic-function methods on Gibbons–Hawking and Taub–NUT bases, and it derives corrected attractor geometries with AdS$_2$ or AdS$_3$ near-horizon factors. Entropy is computed using entropy-function and c-extremization techniques, including the impact of higher-derivative corrections, with special attention to the 4D/5D connection and the emergence of a modified charge dictionary from delocalized sources. The findings illuminate how quantum/string effects smooth certain small black hole/string singularities, refine the relationship between 4D and 5D solutions, and highlight open questions for black rings and higher dimensions in string theory.

Abstract

We review recent developments in understanding quantum/string corrections to BPS black holes and strings in five-dimensional supergravity. These objects are solutions to the effective action obtained from M-theory compactified on a Calabi-Yau threefold, including the one-loop corrections determined by anomaly cancellation and supersymmetry. We introduce the off-shell formulation of this theory obtained through the conformal supergravity method and review the methods for investigating supersymmetric solutions. This leads to quantum/string corrected attractor geometries, as well as asymptotically flat black strings and spinning black holes. With these solutions in hand, we compare our results with analogous studies in four-dimensional string-corrected supergravity, emphasizing the distinctions between the four and five dimensional theories.

Figures (2)

• Figure 1: Numerical solution of equation (\ref{['K3eq3']}); the curve represents $e^{-2U(r)}$ for small values of $r$. The oscillatory behavior is characteristic of higher derivative theories and will be discussed further in Section \ref{['farstring']}.
• Figure 2: Analytical and numerical results for $\Delta(r)$ in the near string region. The solid curve describes the numerical solution of (\ref{['bni']}). The dotted curve represent the analytical solution for small values of r given by (\ref{['bnj']}), and the dashed curved is the approximate solution for large values of r (\ref{['bnk']}).