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

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 $α'$-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.

Figures (9)

• Figure 1: Integration contour in the complex s-plane employed to evaluate the loop integral \ref{['contourIntgral']}. The non-perturbative singularities lie along \ref{['nonPertPolesGeneral']}, whereas the perturbative ones fall onto the real axis. In the limit $\text{Re}\, \alpha \rightarrow 0$, all the poles become real.
• Figure 2: Penrose diagrams of AdS spacetimes in different coordinate systems. The triangular region corresponds to that associated to the Poincaré patch, cf. eq. \ref{['eq:conformalcoords']}. The red dotted lines denote constant $\rho$ slices. The global patch, on the other hand, is generated by an infinite array of consecutive Poincaré slices. Notice that the latter includes two boundaries, unlike AdS$_d$ with $d>2$.
• Figure 3: Penrose diagrams for $\textbf{(a)}$ extremal Reissner-Nördstrom black hole and $\textbf{(b)}$ global AdS$_2$. The near-horizon region corresponds to the shaded (gray) area in the left image.
• Figure 4: Schematic depiction of the geodesic trajectory of a charged particle living on a 2-sphere with a constant and everywhere orthogonal magnetic field. The orbit (black) precesses around a conserved generalized angular momentum vector $\boldsymbol{J} = j\, \partial_z$ at a polar angle fixed by $\cos \theta = -q_m/j$.
• Figure 5: Effective scalar potential $V(\rho)$ controlling the radial dynamics in AdS$_2$ after solving the motion along the sphere. A dashed vertical line (red) at $\rho=0$ denotes the timelike boundary of anti-de Sitter. The qualitative features of the potential depend on whether $\textbf{(a)}$$q_e^2 <\tilde{m}^2 + \ell^2$ (subextremal), $\textbf{(b)}$$q_e^2 >\tilde{m}^2+ \ell^2$ (superextremal), or $\textbf{(c)}$$q_e^2 =\tilde{m}^2 +\ell^2$ (extremal). In each case, we show the corresponding effective potential for both relative signs of the energy $E$ and the electric charge $q_e$, namely for $E q_e>0$ (yellow) and $E q_e<0$ (blue). Notice that sending $q_e \to -q_e$ with fixed $E$ amounts to the map $\rho \to -\rho$, as can be easily verified from the explicit definition of $V(\rho)$ in eq. \ref{['eq:genradialeq']}.