Rigid 6D supersymmetry and localization

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 Kaehler with torsion. As an application, we show that the path integral of pure super Yang-Mills theory defined on a Calabi-Yau threefold M_6 localizes on stable holomorphic bundles over M_6.

31 pages

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Cited by in corpus (22)

• Supersymmetry on Curved Spaces and Holography
• Top Down Approach to 6D SCFTs
• Exact Results in Supersymmetric Field Theories on Manifolds with Boundaries
• Extended Supersymmetry on Curved Spaces
• Supersymmetry on curved spaces and superconformal anomalies
• Supercurrent anomalies in 4d SCFTs
• Supersymmetry on Three-dimensional Lorentzian Curved Spaces and Black Hole Holography
• Introduction to localization in quantum field theory
• Supersymmetry anomalies in $\mathcal{N}=1$ conformal supergravity
• Killing superalgebras for Lorentzian four-manifolds
• Superconformal quantum field theory in curved spacetime
• Conformal symmetry superalgebras
• One-loop tests of supersymmetric gauge theories on spheres
• On $\mathcal{N}=4$ supersymmetry enhancements in three dimensions
• Supersymmetry anomalies in new minimal supergravity
• Killing superalgebras for Lorentzian six-manifolds
• Supersymmetric branes on curved spaces and fluxes
• Curvature Couplings in $\mathcal{N}=(2,2)$ Nonlinear Sigma Models on $S^2$
• Supersymmetric branes and instantons on curved spaces
• (1,0) gauge theories on the six-sphere
• Submaximal conformal symmetry superalgebras for Lorentzian manifolds of low dimension
• Supersymmetric Yang-Mills theory on conformal supergravity backgrounds in ten dimensions