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Holomorphic Anomaly in Gauge Theory on ALE space

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Abstract

We consider four-dimensional Ω-deformed \({\mathcal{N} = 2}\) supersymmetric SU(2) gauge theory on A 1 space and its lift to five dimensions. We find that the partition functions can be reproduced via special geometry and the holomorphic anomaly equation. Schwinger-type integral expressions for the boundary conditions at the monopole/dyon point in moduli space are inferred. The interpretation of the five-dimensional partition function as the partition function of a refined topological string on A 1 × (local \({\mathbb{P}^{1} \times \mathbb{P}^1}\)) is suggested.

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  1. Center for Theoretical Physics, University of California, Berkeley, USA

    Daniel Krefl & Sheng-Yu Darren Shih

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  1. Daniel Krefl
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  2. Sheng-Yu Darren Shih
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Correspondence to Daniel Krefl.

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Krefl, D., Shih, SY.D. Holomorphic Anomaly in Gauge Theory on ALE space. Lett Math Phys 103, 817–841 (2013). https://doi.org/10.1007/s11005-013-0617-6

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