Supergravity flows and D-brane stability

TL;DR

The paper analyzes how BPS states in type II string theory on a Calabi–Yau manifold correspond to BPS supergravity solutions, uncovering puzzles that arise when a single localized charge is assumed. It resolves these by introducing composite configurations and forked attractor flows, yielding a smooth EFT picture of decay at marginal stability and connecting to Joyce transitions and $\Pi$-stability. By extending to multicenter, stationary solutions, it explains how angular momentum and nonlocal charge interactions shape the spectrum and stability of BPS states. The work links geometric notions (special Lagrangian submanifolds, Joyce transitions) with stringy D-brane pictures (3-pronged strings) and provides a framework for understanding marginal stability in a controlled supergravity setting, with potential implications for black hole entropy and moduli-space dynamics.

Abstract

We investigate the correspondence between existence/stability of BPS states in type II string theory compactified on a Calabi-Yau manifold and BPS solutions of four dimensional N=2 supergravity. Some paradoxes emerge, and we propose a resolution by considering composite configurations. This in turn gives a smooth effective field theory description of decay at marginal stability. We also discuss the connection with 3-pronged strings, the Joyce transition of special Lagrangian submanifolds, and Pi-stability.

Figures (13)

• Figure 1: Typical case sketch of the potential $-e^{2U} V$ in which the effective particle is moving, plotted as a function of $e^{2U}$ and the moduli $z$. Of the three plotted trajectories, only (c) satisfies the required asymptotic conditions yielding a BPS black hole.
• Figure 2: Typical flow gradient field in moduli space (represented here by the $z$-plane) close to a generic attractor point with nonzero minimal $|Z|$. The gradient vectors vanish at the attractor point.
• Figure 3: Energy density sketch of an "empty hole".
• Figure 4: Flow gradient field in the $Y=\int_{\Gamma} \Omega_0$-plane close to a regular point $Y=0$ in moduli space where the central charge vanishes. The gradient vectors do not vanish at the attractor point, leading to a breakdown of the flow.
• Figure 5: Some surfaces of equal $\tau$ in the 2-center case.