Crossing the Wall: Branes vs. Bundles

Abstract

We test a recently proposed wall-crossing formula for the change of the Hilbert space of BPS states in d=4,N=2 theories. We study decays of D4D2D0 systems into pairs of D4D2D0 systems and we show how the wall-crossing formula reproduces results of Goettsche and Yoshioka on wall-crossing behavior of the moduli of slope-stable holomorphic bundles over holomorphic surfaces. Our comparison shows very clearly that the moduli space of the D4D2D0 system on a rigid surface in a Calabi-Yau is not the same as the moduli space of torsion free sheaves, even when worldhseet instantons are neglected. Moreover, we argue that the physical formula should make some new mathematical predictions for a future theory of the moduli of stable objects in the derived category.

23pp. latex, one figure

References in corpus (17)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Black Hole Attractors and the Topological String
• Vector Bundles And F Theory
• I-Brane Inflow and Anomalous Couplings on D-Branes
• On Classification of N=2 Supersymmetric Theories, (e-mail uncorrupted version)
• A New Supersymmetric Index
• Vector Bundles over Elliptic Fibrations
• Holomorphic Vector Bundles and Non-Perturbative Vacua in M-Theory
• D-Brane Stability and Monodromy
• Stability conditions on triangulated categories
• On the correspondence between D-branes and stationary supergravity solutions of type II Calabi-Yau compactifications
• The Geometry Underlying Mirror Symmetry
• Fourier-Mukai Transform and Mirror Symmetry for D-Branes on Elliptic Calabi-Yau
• Fibrewise T-Duality for D-Branes on Elliptic Calabi-Yau
• Taniguchi Lecture on Principal Bundles on Elliptic Fibrations
• Moduli stacks and invariants of semistable objects on K3 surfaces
• Moduli of stable objects in a triangulated category

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