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3D-partition functions on the sphere: exact evaluation and mirror symmetry
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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.
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Five-brane webs, 3d $\mathcal{N}=2$ theories and quantum curves
The Newton polygon of the quantum curve for a 3d N=2 brane configuration is conjectured to equal the toric diagram dual to its (p,q) 5-brane web, with derivations for Lagrangian cases and new matrix models for p>=2.
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