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B-Model Approach to Instanton Counting

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New Dualities of Supersymmetric Gauge Theories

Part of the book series: Mathematical Physics Studies ((MPST))

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Abstract

The instanton partition function of \(\mathcal{N}=2\) gauge theory in the general \(\Omega \)-background is, in a suitable analytic continuation, a solution of the holomorphic anomaly equation known from B-model topological strings. The present review of this connection is a contribution to a special volume on recent developments in \(\mathcal{N}=2\) supersymmetric gauge theory and the 2d-4d relation, edited by J. Teschner.

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Notes

  1. 1.

    This is not to say that the microscopic origin of the holomorphic anomaly might not be better explained in the two-parameter scheme, see [27].

  2. 2.

    As is now evident, the constant is a third solution of the differential equation. This solution decouples in special cases, such as SU(2) gauge theory with massless hypermultiplets.

  3. 3.

    It that sense, the singularity structure (but not the regular terms) in those strong coupling regions does follow from a field theory computation.

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Acknowledgments

We would like to thank J. Teschner for the invitation to participate in this joint review effort, his hard work and patience. We thank all other contributors for their valuable comments and input. The work of D.K. has been supported in part by a Simons fellowship, the Berkeley Center for Theoretical Physics and the National Research Foundation of Korea Grant No. 2012R1A2A2A02046739. The research of J.W. is supported in part by an NSERC discovery grant and a Tier II Canada Research Chair.

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Authors and Affiliations

  1. Center for Theoretical Physics, Seoul National University, Seoul, South Korea

    Daniel Krefl

  2. Department of Physics and Department of Mathematics and Statistics, McGill University, Montreal, QC, Canada

    Johannes Walcher

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  1. Daniel Krefl
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Correspondence to Daniel Krefl .

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Editors and Affiliations

  1. String Theory Group, DESY String Theory Group, Hamburg, Hamburg, Germany

    Jörg Teschner

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Krefl, D., Walcher, J. (2016). B-Model Approach to Instanton Counting. In: Teschner, J. (eds) New Dualities of Supersymmetric Gauge Theories. Mathematical Physics Studies. Springer, Cham. https://doi.org/10.1007/978-3-319-18769-3_14

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