Wall-crossing of D4-D2-D0 and flop of the conifold
Takahiro Nishinaka, Satoshi Yamaguchi
TL;DR
This paper investigates how BPS states of D4-D2-D0 branes change across different stability regions on the conifold, using wall-crossing formulas to relate degeneracies before and after a flop transition.
Contribution
It applies the Kontsevich-Soibelman wall-crossing formula to the conifold, establishing relations between BPS degeneracies in different chambers and predicting degeneracies in all chambers.
Findings
Derived relations between BPS degeneracies across the flop transition
Confirmed consistency with known results in special chambers
Predicted BPS degeneracies in all chambers
Abstract
We discuss the wall-crossing of the BPS bound states of a non-compact holomorphic D4-brane with D2 and D0-branes on the conifold. We use the Kontsevich-Soibelman wall-crossing formula and analyze the BPS degeneracy in various chambers. In particular we obtain a relation between BPS degeneracies in two limiting attractor chambers related by a flop transition. Our result is consistent with known results and predicts BPS degeneracies in all chambers.
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