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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References

SHOWING 1-10 OF 48 REFERENCES
Holomorphic anomaly in gauge theories and matrix models
We use the holomorphic anomaly equation to solve the gravitational corrections to Seiberg-Witten theory and a two-cut matrix model, which is related by the Dijkgraaf-Vafa conjecture to the
Vortex Counting and Lagrangian 3-Manifolds
To every 3-manifold M one can associate a two-dimensional $${\mathcal{N}=(2, 2)}$$ supersymmetric field theory by compactifying five-dimensional $${\mathcal{N}=2}$$ super-Yang–Mills theory on M. This
Loop and surface operators in $ \mathcal{N} = 2 $ gauge theory and Liouville modular geometry
Recently, a duality between Liouville theory and four dimensional $ \mathcal{N} = 2 $ gauge theory has been uncovered by some of the authors. We consider the role of extended objects in gauge theory,
The Real Topological String on a local Calabi-Yau
We study the topological string on local P2 with O-plane and D-brane at its real locus, using three complementary techniques. In the A-model, we refine localization on the moduli space of maps with
The Real Topological Vertex at Work
Lectures on instanton counting
These notes have two parts. The first is a study of Nekrasov's deformed partition functions $Z(\ve_1,\ve_2,\vec{a}:\q,\vec{\tau})$ of N=2 SUSY Yang-Mills theories, which are generating functions of
M theory and topological strings. 2.
The $R^2 F^{2g-2}$ terms of Type IIA strings on Calabi-Yau 3-folds, which are given by the corresponding topological string amplitudes (a worldsheet instanton sum for all genera), are shown to have a
Direct integration of the topological string
We present a new method to solve the holomorphic anomaly equations governing the free energies of type B topological strings. The method is based on direct integration with respect to the
Evidence for Tadpole Cancellation in the Topological String
We study the topological string on compact Calabi-Yau threefolds in the presence of orientifolds and D-branes. In examples, we find that the total topological string amplitude admits a BPS expansion
...
1
2
3
4
5
...