Split attractor flows and the spectrum of BPS D-branes on the Quintic

TL;DR

This work leverages four-dimensional ${\mathcal N}=2$ supergravity and split attractor flows to map the spectrum of BPS D-branes on the quintic Calabi–Yau, connecting macroscopic flow structures to microscopic BPS states. It combines a numerical analysis with large-radius analytical benchmarks to predict the presence or absence of charges in moduli-space regions, locate lines of marginal stability, and reveal multiple basins of attraction induced by conifold singularities. A central result is the existence of a moduli-space–dependent spectrum with a universal area bound for the cores of BPS states, and a marked distinction between large-radius and Gepner-point physics evidenced by explicit decay and bound-state examples. The study demonstrates that the split-flow picture provides detailed, quantitative insights into BPS spectra, including stability criteria, monodromy effects, and spacetime structure, while highlighting the ongoing need to connect these supergravity insights with full string-theoretic (microscopic) underpinnings. The quintic analysis shows a rich landscape of states, with infinite spectrum, discrete masses, and diverse realizations (single-center black holes, bound states, empty-hole constituents), underscoring the predictive power and limitations of the split-flow approach for complex Calabi–Yau compactifications.

Abstract

We investigate the spectrum of type IIA BPS D-branes on the quintic from a four dimensional supergravity perspective and the associated split attractor flow picture. We obtain some very concrete properties of the (quantum corrected) spectrum, mainly based on an extensive numerical analysis, and to a lesser extent on exact results in the large radius approximation. We predict the presence and absence of some charges in the BPS spectrum in various regions of moduli space, including the precise location of the lines of marginal stability and the corresponding decay products. We explain how the generic appearance of multiple basins of attraction is due to the presence of conifold singularities and give some specific examples of this phenomenon. Some interesting space-time features of these states are also uncovered, such as a nontrivial, moduli independent lower bound on the area of the core of arbitrary BPS solutions, whether they are black holes, empty holes, or more complicated composites.