Wall crossing in local Calabi Yau manifolds

2008/10/27 by Daniel L. Jafferis, Jafferis, Daniel L., Gregory W. Moore +1 · 3 citations
Mathematics · #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #High Energy Physics - Theory (hep-th)

paper · pdf · doi:10.48550/arxiv.0810.4909

openalex publication_date 2008/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the BPS states of a D6-brane wrapping the conifold and bound to collections of D2 and D0 branes. We find that in addition to the complexified Kahler parameter of the rigid sphere it is necessary to introduce an extra real parameter to describe BPS partition functions and marginal stability walls. The supergravity approach to BPS state-counting gives a simple derivation of results of Szendroi concerning Donaldson-Thomas theory on the noncommutative conifold. This example also illustrates some interesting limitations on the supergravity approach to BPS state-counting and wall-crossing.

Citations

• Crossing the Wall: Branes vs. Bundles
• Two Dimensional Yang-Mills, Black Holes and Topological Strings
• Arithmetic and Attractors
• On the correspondence between D-branes and stationary supergravity solutions of type II Calabi-Yau compactifications
• Derived categories of small toric Calabi-Yau 3-folds and counting invariants
• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Quantum Calabi-Yau and Classical Crystals
• Computing a pyramid partition generating function with dimer shuffling

Cited by

• GW/DT invariants and 5D BPS indices for strips from topological recursion
• Super Macdonald polynomials and BPS state counting on the blow-up
• Equivalence of Three Wall Crossing Formulae

Related

• Crossing the Wall: Branes vs. Bundles
• Wall-crossing, Toric divisor and Seiberg duality
• Affine SU(N) algebra from wall-crossings
• Wall-crossing, Hitchin Systems, and the WKB Approximation
• BPS Wall Crossing and Topological Strings