Multiple D4-D2-D0 on the Conifold and Wall-crossing with the Flop

TL;DR

This paper investigates the wall-crossing behavior of D4-D2-D0 bound states on the conifold, revealing how BPS indices change across stability walls and connecting different large radius limits through flop transitions.

Contribution

It identifies the walls of marginal stability for D4-D2-D0 states on the conifold and applies the Kontsevich-Soibelman formula to compute index changes, linking different large radius phases.

Findings

Wall-crossing formulas describe BPS index changes.

Field theories on D4-branes are connected via flop transitions.

Stable bound states of D4-D2-D0 exist in certain limits.

Abstract

We study the wall-crossing phenomena of D4-D2-D0 bound states with two units of D4-brane charge on the resolved conifold. We identify the walls of marginal stability and evaluate the discrete changes of the BPS indices by using the Kontsevich-Soibelman wall-crossing formula. In particular, we find that the field theories on D4-branes in two large radius limits are properly connected by the wall-crossings involving the flop transition of the conifold. We also find that in one of the large radius limits there are stable bound states of two D4-D2-D0 fragments.