Abstract
We construct rigid supersymmetric theories for interacting vector and tensor multiplets on six-dimensional Riemannian spin manifolds. Analyzing the Killing spinor equations, we derive the constraints on these theories. To this end, we reformulate the conditions for supersymmetry as a set of necessary and sufficient conditions on the geometry. The formalism is illustrated with a number of examples, including manifolds that are hermitian, strong Kähler with torsion. As an application, we show that the path integral of pure super Yang-Mills theory defined on a Calabi-Yau threefold \( {{\mathcal{M}}_6} \) localizes on stable holomorphic bundles over \( {{\mathcal{M}}_6} \).
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ArXiv ePrint: 1212.4706
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Samtleben, H., Sezgin, E. & Tsimpis, D. Rigid 6D supersymmetry and localization. J. High Energ. Phys. 2013, 137 (2013). https://doi.org/10.1007/JHEP03(2013)137
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DOI: https://doi.org/10.1007/JHEP03(2013)137