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3D-partition functions on the sphere: exact evaluation and mirror symmetry

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Abstract

We study \( \mathcal{N} = {4} \) quiver theories on the three-sphere. We compute partition functions using the localisation method by Kapustin et al. solving exactly the matrix integrals at finite N, as functions of mass and Fayet-Iliopoulos parameters. We find a simple explicit formula for the partition function of the quiver tail T(SU(N)). This formula opens the way for the analysis of star-shaped quivers and their mirrors (that are the Gaiotto-type theories arising from M5 branes on punctured Riemann surfaces). We provide non-perturbative checks of mirror symmetry for infinite classes of theories and find the partition functions of the T N theory, the building block of generalised quiver theories.

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Authors and Affiliations

  1. Theoretical Physics Group, The Blackett Laboratory, Imperial College, Prince Consort Road, London, SW7 2AZ, UK

    Sergio Benvenuti

  2. School of Physics, Queen Mary University of London, Mile End Road, London, E1 4NS, UK

    Sara Pasquetti

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  1. Sergio Benvenuti
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  2. Sara Pasquetti
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Correspondence to Sara Pasquetti.

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ArXiv ePrint: 1105.2551

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Benvenuti, S., Pasquetti, S. 3D-partition functions on the sphere: exact evaluation and mirror symmetry. J. High Energ. Phys. 2012, 99 (2012). https://doi.org/10.1007/JHEP05(2012)099

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