Rigidly Supersymmetric Gauge Theories on Curved Superspace

Abstract

In this note we construct rigidly supersymmetric gauged sigma models and gauge theories on certain Einstein four-manifolds, and discuss constraints on these theories. In work elsewhere, it was recently shown that on some nontrivial Einstein four-manifolds such as AdS${}_4$, N=1 rigidly supersymmetric sigma models are constrained to have target spaces with exact Kähler forms. Similarly, in gauged sigma models and gauge theories, we find that supersymmetry imposes constraints on Fayet-Iliopoulos parameters, which have the effect of enforcing that Kähler forms on quotient spaces be exact. We also discuss general aspects of universality classes of gauged sigma models, as encoded by stacks, and also discuss affine bundle structures implicit in these constructions.

23 pages; references added; more discussion added; v4: typos fixed

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Cited by in corpus (30)

• Supersymmetry on Curved Spaces and Holography
• Exploring Curved Superspace
• Seiberg-Witten Theories on Ellipsoids
• Extended Supersymmetry on Curved Spaces
• Exploring Curved Superspace (II)
• Rigid supersymmetric theories in 4d Riemannian space
• Supersymmetry on Three-dimensional Lorentzian Curved Spaces and Black Hole Holography
• Three-dimensional N=2 supergravity theories: From superspace to components
• Rigid Supersymmetric Backgrounds of Minimal Off-Shell Supergravity
• Global Supersymmetry on Curved Spaces in Various Dimensions
• Rigid 6D supersymmetry and localization
• Symmetries of curved superspace in five dimensions
• Symmetries of curved superspace
• Rigid 4D N=2 supersymmetric backgrounds and actions
• Symmetries of supergravity backgrounds and supersymmetric field theory
• Supersymmetric backgrounds from 5d N=1 supergravity
• Killing superalgebras for Lorentzian four-manifolds
• Superconformal quantum field theory in curved spacetime
• Nonlinear sigma models with AdS supersymmetry in three dimensions
• Conformal symmetry superalgebras
• Killing superalgebras for Lorentzian six-manifolds
• Rigid Supersymmetric Backgrounds of 3-dimensional Newton-Cartan Supergravity
• Supersymmetric branes on curved spaces and fluxes
• Curvature Couplings in $\mathcal{N}=(2,2)$ Nonlinear Sigma Models on $S^2$
• Supersymmetric gauge theory on curved 7-branes
• Supersymmetric branes and instantons on curved spaces
• Self-consistency of Conformally Coupled ABJM Theory at the Quantum Level
• Ten-dimensional lifts of global supersymmetry on curved spaces
• N=(4,4) Vector Multiplets on Curved Two-Manifolds
• Supersymmetric Yang-Mills theory on conformal supergravity backgrounds in ten dimensions