Extended Holomorphic Anomaly in Gauge Theory

@article{Krefl2011ExtendedHA,
  title={Extended Holomorphic Anomaly in Gauge Theory},
  author={Daniel Krefl and Johannes Walcher},
  journal={Letters in Mathematical Physics},
  year={2011},
  volume={95},
  pages={67-88}
}
The partition function of an $${\mathcal {N}=2}$$ gauge theory in the Ω-background satisfies, for generic value of the parameter $${\beta=-{\epsilon_1}/{\epsilon_2}}$$ , the, in general extended, but otherwise β-independent, holomorphic anomaly equation of special geometry. Modularity together with the (β-dependent) gap structure at the various singular loci in the moduli space completely fixes the holomorphic ambiguity, also when the extension is non-trivial. In some cases, the theory at the… 
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