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June 2012 Direct integration for general $\Omega$ backgrounds
Min-xin Huang, Albrecht Klemm
Adv. Theor. Math. Phys. 16(3): 805-849 (June 2012).


We extend the direct integration method of the holomorphic anomalyequations to general $\Omega$ backgrounds $\epsilon_1\neq -\epsilon_2$for pure SU(2) $N=2$ Super-Yang-Mills theory and topological stringtheory on non-compact Calabi-Yau threefolds. We find that anextension of the holomorphic anomaly equation, modularity and boundary conditions provided by the perturbative terms as well as by the gap condition at the conifold are sufficient to solve the generalized theory in the above cases. In particular, we use the method to solve the topological string for the general $\Omega$ backgrounds on non-compact toric Calabi-Yau spaces. The conifold boundary condition follows from that the $N=2$ Schwinger-loop calculation with Bogomol'nyi-Prasad-Sommerfield (BPS) states coupled to a self-dual and an anti-self-dual field strength. We calculate such BPS states also for the large base decompactification limit of Calabi-Yau spaces with regular $K3$ fibrations and half $K3$s embedded in Calabi-Yau backgrounds.


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Min-xin Huang. Albrecht Klemm. "Direct integration for general $\Omega$ backgrounds." Adv. Theor. Math. Phys. 16 (3) 805 - 849, June 2012.


Published: June 2012
First available in Project Euclid: 20 March 2013

zbMATH: 1276.81098
MathSciNet: MR3024275

Rights: Copyright © 2012 International Press of Boston


Vol.16 • No. 3 • June 2012
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