Quantum Calabi-Yau Black Holes and Non-Perturbative D0-brane Effects

TL;DR

This paper calculates the entropy of 4d BPS black holes in string theory, including all leading quantum corrections, revealing both perturbative and non-perturbative effects and their dependence on gauge configurations.

Contribution

It provides a comprehensive analysis of quantum and non-perturbative D0-brane effects on black hole entropy in Calabi-Yau compactifications, including conditions where these effects vanish.

Findings

Quantum corrections modify black hole entropy.

Non-perturbative effects depend on gauge backgrounds.

Certain configurations suppress non-perturbative contributions.

Abstract

We compute the supersymmetric entropy of the most general BPS black hole in 4d $\mathcal{N}=2$ supergravity coupled to $n_V$ vector multiplets obtained from Type IIA string theory compactified on a Calabi-Yau threefold at large volume, including the all-genera leading-order $\alpha'$-corrections. These can be equivalently seen as D0-brane quantum effects from a dual five-dimensional M-theory perspective. We find that these corrections generically lead to both perturbative and non-perturbative contributions to the black hole entropy. We argue that the exception occurs for certain specific configurations where the gauge background, seen through the lens of D0-brane probes, behaves as purely electric or purely magnetic, thereby accounting for the absence of such non-perturbative effects. To explore this further, we perform a semiclassical analysis of the (non-)BPS particle dynamics in the near-horizon geometry of the underlying black hole, which is described by a maximally supersymmetric AdS$_2\times \mathbf{S}^2$ solution. As a byproduct, this study provides additional insights into the (non-perturbative) stability of supersymmetric black hole solutions and suggests an interpretation in terms of complex saddles contributing to the worldline path integral.