How to (Non-)Perturb a BPS Black Hole

TL;DR

This paper explores how non-perturbative corrections to BPS black hole observables are governed by probe charged particles in near-horizon geometries, linking string theory computations with black hole physics.

Contribution

It explicitly connects non-perturbative corrections in supergravity to the behavior of probe branes and topological string theory calculations in black hole backgrounds.

Findings

Reproduces Gopakumar--Vafa integral in black hole attractor geometry.

Shows light D-brane states control higher derivative corrections.

Provides a semiclassical understanding of non-perturbative effects.

Abstract

We relate the structure of non-perturbative corrections to BPS black hole observables in flat-spacetime theories with certain properties of probe charged particles in the near-horizon geometry. Concretely, we consider 4d $\mathcal{N} = 2$ supergravity with an infinite tower of F-terms and probe branes in $\text{AdS}_2\times \mathbf{S}^2$ backgrounds threaded by constant electric-magnetic fields. The higher dimensional operators we pick are computed by Type II topological string theory, and we approximate them via the constant map contribution, which is valid at large volume and can be interpreted as arising from D0-branes integrated out in M-theory on a Calabi-Yau threefold times a circle. We analyze the resulting force conditions on massive particles carrying $(q_A, p^A)$ charges, their classical trajectories, and the 1-loop effective action they produce. A simple semiclassical analysis allows us to understand qualitatively the structure of the non-perturbative corrections. The exact path integral assessment then reproduces the Gopakumar--Vafa integral of the flat-spacetime theory, now evaluated in the black hole attractor geometry. Thus, we make explicit how the physics of the fully backreacted black hole solution is controlled by the behaviour of the light D-brane states which generate the relevant set of higher derivative corrections.