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Localization for ${\cal N}=2$ Supersymmetric Gauge Theories in Four Dimensions

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arxiv 1412.7134 v2 pith:JHELZBYX submitted 2014-12-22 hep-th

classification hep-th
keywords supersymmetrictheoriesbackgroundsdimensionsfourgaugelocalizationmathcal
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abstract

This is the 5th article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J. Teschner. We review the supersymmetric localization of $\mathcal{N}=2$ theories on curved backgrounds in four dimensions using $\mathcal{N}=2$ supergravity and generalised conformal Killing spinors. We review some known backgrounds and give examples of new geometries such as local $T^2$-bundle fibrations. We discuss in detail a topological four-sphere with generic $T^2$-invariant metric.

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  1. Topological Twisting of 4d $\mathcal{N}=2$ Supersymmetric Field Theories

    hep-th 2024-11 conditional novelty 8.0 of 10

    For any 4d N=2 theory, topologically twisted partition functions depend on the diffeomorphism type, 't Hooft fluxes, and a generalized spin-c structure.

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