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

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• Quiver Yangian and Supersymmetric Quantum Mechanics
• Bound state transformation walls
• Open BPS Wall Crossing and M-theory
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• Rank Two ADHM Invariants and Wallcrossing
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• BPS State Counting in Local Obstructed Curves from Quiver Theory and Seiberg Duality
• Refined open non-commutative Donaldson-Thomas invariants for small crepant resolutions
• Quiver Yangians and Crystal Melting: A Concise Summary
• Statistical model and BPS D4-D2-D0 counting
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• The Non-commutative Topological Vertex and Wall Crossing Phenomena
• Wall Crossing Phenomenology of Orientifolds
• Equivalence of Three Wall Crossing Formulae
• On the M2-Brane Index on Noncommutative Crepant Resolutions
• Matrix models and stochastic growth in Donaldson-Thomas theory
• Probing Geometry with Stability Conditions
• On Framed Quivers, BPS Invariants and Defects
• q-Deformed Oscillators and D-branes on Conifold
• Attractor invariants, brane tilings and crystals
• Affine SU(N) algebra from wall-crossings
• BPS Spectra, Barcodes and Walls
• Geometry and Combinatorics of Crystal Melting
• On Some Computations of Higher Rank Refined Donaldson-Thomas Invariants
• Wall-crossing, Toric divisor and Seiberg duality
• Topics in Open Topological Strings