Wall-crossing, Toric divisor and Seiberg duality

TL;DR

This paper investigates wall-crossing phenomena of BPS states on the conifold and orbifold C^2/Z_2, linking quiver quantum mechanics, Seiberg duality, and algebraic structures to understand BPS index variations.

Contribution

It provides a detailed analysis of wall-crossing in D4-D2-D0 states, highlighting the role of Seiberg duality and superpotential effects, extending previous D6-D2-D0 studies.

Findings

Wall-crossing relates to Seiberg dualities in quiver quantum mechanics.

Flop transitions affect duality cascades on the conifold.

Witten index generating functions match affine SU(2) characters on orbifolds.

Abstract

We study the wall-crossing phenomena of BPS D4-D2-D0 states on the conifold and orbifold C^2/Z_2, from the viewpoint of the quiver quantum mechanics on the D-branes. The Kahler moduli dependence of the BPS index is translated into the FI parameter dependence of the Witten index. The wall-crossing phenomena are related to the Seiberg dualities of the quiver quantum mechanics. All the differences from the D6-D2-D0 case arise from the additional superpotential and "anti-quark" induced by the D4-brane. When the D-branes are on the conifold, the flop transition changes the duality cascade. When the D-branes are on the orbifold C^2/Z_2, the generating function of the Witten index is always given by a character of the affine SU(2) algebra. Both are consistent with the wall-crossing formula for BPS indices.