Crossing the wall: Branes versus bundles

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21 Scopus citations


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, 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 G̈ottsche 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.

Original languageEnglish (US)
Pages (from-to)1621-1650
Number of pages30
JournalAdvances in Theoretical and Mathematical Physics
Issue number6
StatePublished - Dec 2010

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Physics and Astronomy(all)


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