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Gauge Theories on ALE Space and Super Liouville Correlation Functions

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Abstract

We present a relation between \({\mathcal{N}=2}\) quiver gauge theories on the ALE space \({\mathcal{O}_{\mathbb{P}^1}(-2)}\) and correlators of \({\mathcal{N}=1}\) super Liouville conformal field theory, providing checks in the case of punctured spheres and tori. We derive a blow-up formula for the full Nekrasov partition function and show that, up to a U(1) factor, the \({\mathcal{N}=2^*}\) instanton partition function is given by the product of the character of \({\widehat{SU}(2)_2}\) times the super Virasoro conformal block on the torus with one puncture. Moreover, we match the perturbative gauge theory contribution with super Liouville three-point functions.

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Authors and Affiliations

  1. International School of Advanced Studies (SISSA), via Bonomea 265, 34136, Trieste, Italy

    Giulio Bonelli, Kazunobu Maruyoshi & Alessandro Tanzini

  2. INFN, Sezione di Trieste, Trieste, Italy

    Giulio Bonelli, Kazunobu Maruyoshi & Alessandro Tanzini

  3. I.C.T.P., Strada Costiera 11, 34014, Trieste, Italy

    Giulio Bonelli

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  1. Giulio Bonelli
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Correspondence to Kazunobu Maruyoshi.

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Bonelli, G., Maruyoshi, K. & Tanzini, A. Gauge Theories on ALE Space and Super Liouville Correlation Functions. Lett Math Phys 101, 103–124 (2012). https://doi.org/10.1007/s11005-012-0553-x

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  • DOI: https://doi.org/10.1007/s11005-012-0553-x

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