On the correspondence between D-branes and stationary supergravity solutions of type II Calabi-Yau compactifications

TL;DR

This work investigates the mapping between D-brane BPS states in type II Calabi–Yau compactifications and four-dimensional stationary N=2 supergravity solutions, extending beyond simple black holes to multicenter configurations. By formulating and solving generalized BPS equations, it shows that BPS states can be realized as stable multicenter solitons with intrinsically nonlocal charges, governed by attractor flows and marginal stability surfaces. Key results include a split-flow picture in moduli space, explicit analysis of layered shell configurations, and a general framework for constructing and understanding multicenter solutions with nonzero angular momentum. The findings suggest a powerful correspondence that could systematize the D-brane spectrum in Calabi–Yau compactifications and hint at deeper connections to stability concepts and potential dual descriptions.

Abstract

In this talk, I review how four dimensional stationary supergravity solutions that are more general than spherically symmetric black holes emerge naturally in the low energy description of BPS states in type II Calabi-Yau compactifications. An explicit construction of multicenter solutions using single center attractor flows as building blocks is presented, and some interesting properties of these solutions are examined. We end with a brief remark on non-BPS configurations.