Strings, higher curvature corrections, and black holes

TL;DR

The work surveys how string theory accounts for black hole entropy beyond the leading area term by incorporating higher-derivative corrections via the Weyl multiplet and by exploiting the attractor mechanism in $\mathcal{N}=2$ supergravity. It highlights the OSV framework, which links macroscopic entropy to a black hole free energy and ties the entropy to the topological string partition function, effectively treating the problem in a mixed ensemble and, in favorable cases, achieving remarkable agreement with microscopic state counting for BPS black holes. The analysis covers both small and large BPS black holes, showing how subleading corrections—from $F^{(g)}$ terms to non-holomorphic and instanton contributions—match between macroscopic and microscopic calculations, while pointing to subtleties in ensemble definitions and duality constraints. The discussion also connects black hole physics to flux compactifications and quantum cosmology, proposing a minisuperspace viewpoint via the topological string wave function and outlining open questions for exact OSV validity and non-supersymmetric generalizations.

Abstract

We review old and recent results on subleading contributions to black hole entropy in string theory.