(Dis)assembling Special Lagrangians

TL;DR

This paper provides a microscopic explanation for split attractor flows in N=2 supergravity, linking them to the geometry of special Lagrangian submanifolds in Calabi-Yau compactifications, and offers methods to analyze their stability and moduli.

Contribution

It introduces a geometric approach to disassemble and assemble special Lagrangians, aiding in understanding stability walls and moduli spaces without homological algebra.

Findings

Provides a microscopic explanation for split attractor flows.

Offers a geometric method to analyze special Lagrangians.

Enables determination of marginal stability walls and moduli spaces.

Abstract

We explain microscopically why split attractor flows, known to underlie certain stationary BPS solutions of four dimensional N=2 supergravity, are the relevant data to describe wrapped D-branes in Calabi-Yau compactifications of type II string theory. We work entirely in the context of the classical geometry of A-branes, i.e. special Lagrangian submanifolds, avoiding both the use of homological algebra and explicit constructions of special Lagrangians. Our results provide a way to disassemble and assemble arbitrary special Lagrangians to and from more simple building blocks, giving a concrete way to determine for example marginal stability walls and deformation moduli spaces.