Advances in Theoretical and Mathematical Physics

Wall-crossing of D4-branes using flow trees

Jan Manschot

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Abstract

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 $\Omega(\Gamma)$.

Article information

Source
Adv. Theor. Math. Phys., Volume 15, Number 1 (2011), 1-42.

Dates
First available in Project Euclid: 24 April 2012

Permanent link to this document
https://projecteuclid.org/euclid.atmp/1335278889

Mathematical Reviews number (MathSciNet)
MR2888006

Zentralblatt MATH identifier
1352.81051

Citation

Manschot, Jan. Wall-crossing of D4-branes using flow trees. Adv. Theor. Math. Phys. 15 (2011), no. 1, 1--42. https://projecteuclid.org/euclid.atmp/1335278889


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