Wall crossing in local Calabi Yau manifolds

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.

20pp., 1 figure

References in corpus (5)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Two Dimensional Yang-Mills, Black Holes and Topological Strings
• Crossing the Wall: Branes vs. Bundles
• Computing a pyramid partition generating function with dimer shuffling
• Ample D4-D2-D0 Decay

Cited by in corpus (11)

• Wall-Crossing from Boltzmann Black Hole Halos
• Crystal Melting and Toric Calabi-Yau Manifolds
• Wall Crossing of BPS States on the Conifold from Seiberg Duality and Pyramid Partitions
• Non-perturbative effects and wall-crossing from topological strings
• Geometric engineering of (framed) BPS states
• Statistical model and BPS D4-D2-D0 counting
• BPS spectrum, wall crossing and quantum dilogarithm identity
• Wall Crossing Phenomenology of Orientifolds
• Probing Geometry with Stability Conditions
• Affine SU(N) algebra from wall-crossings
• Topics in Open Topological Strings