Open Access
December 2010 Crossing the wall: branes versus bundles
Duiliu-Emanuel Diaconescu, Gregory W. Moore
Adv. Theor. Math. Phys. 14(6): 1621-1650 (December 2010).


We test a recently proposed wall-crossing formula for the change of the Hilbert space of Bogomol’nyi–Prasad–Sommerfield (BPS) states in $d = 4, \mathcal{N} = 2$ theories. We study decays of $D4D2D0$ systems into pairs of $D4D2D0$ systems and we show how the wall-crossing formula reproduces results of Göttsche 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.


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Duiliu-Emanuel Diaconescu. Gregory W. Moore. "Crossing the wall: branes versus bundles." Adv. Theor. Math. Phys. 14 (6) 1621 - 1650, December 2010.


Published: December 2010
First available in Project Euclid: 24 April 2012

zbMATH: 1245.81159
MathSciNet: MR2872467

Rights: Copyright © 2010 International Press of Boston

Vol.14 • No. 6 • December 2010
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