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

Abstract

We study 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 TN theory, the building block of generalised quiver theories.

30 pages, 12 figures. v2: added references, minor changes

References in corpus (6)

• Notes on SUSY Gauge Theories on Three-Sphere
• S-duality in N=2 supersymmetric gauge theories
• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• Mirrors of 3d Sicilian theories
• From 4d superconformal indices to 3d partition functions
• Superconformal indices of three-dimensional theories related by mirror symmetry

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