Open Access
January 2011 Wall-crossing of D4-branes using flow trees
Jan Manschot
Adv. Theor. Math. Phys. 15(1): 1-42 (January 2011).


The moduli dependence of D4-branes on a Calabi–Yau manifold is studied using attractor flow trees, in the large volume limit of the Kähler cone. One of the moduli-dependent existence criteria of flow trees is the positivity of the flow parameters along its edges. It is shown that the sign of the flow parameters can be determined iteratively as function of the initial moduli, without explicit calculation of the flow of the moduli in the tree. Using this result, an indefinite quadratic form, which appears in the expression for the D4-D2-D0 BPS mass in the large volume limit, is proven to be positive definite for flow trees with 3 or less endpoints. The contribution of these flow trees to the BPS partition function is therefore convergent. From non-primitive wall crossing is deduced that the S-duality invariant partition function must be a generating function of the rational invariants $\bar{\Omega} (\Gamma) = \Sigma_{m|\Gamma} =\frac {\Omega(\Gamma/m)}{m^2}$ instead of the integer invariants $\Omega(\Gamma)$.


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Jan Manschot. "Wall-crossing of D4-branes using flow trees." Adv. Theor. Math. Phys. 15 (1) 1 - 42, January 2011.


Published: January 2011
First available in Project Euclid: 24 April 2012

zbMATH: 1352.81051
MathSciNet: MR2888006

Rights: Copyright © 2011 International Press of Boston

Vol.15 • No. 1 • January 2011
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