Rigid supersymmetric theories in 4d Riemannian space

Abstract

We consider rigid supersymmetric theories in four-dimensional Riemannian spin manifolds. We build the Lagrangian directly in Euclidean signature from the outset, keeping track of potential boundary terms. We reformulate the conditions for supersymmetry as a set of conditions on the torsion classes of a suitable SU(2) or trivial G-structure. We illustrate the formalism with a number of examples including supersymmetric backgrounds with non-vanishing Weyl tensor.

26 pages

References in corpus (4)

• Rigidly Supersymmetric Gauge Theories on Curved Superspace
• Phase Transitions of Large N Orbifold Gauge Theories
• The structure of N=2 supersymmetric nonlinear sigma models in AdS_4
• Generalized geometry, calibrations and supersymmetry in diverse dimensions

Cited by in corpus (41)

• Supersymmetric Field Theories on Three-Manifolds
• The Geometry of Supersymmetric Partition Functions
• Supersymmetry on Curved Spaces and Holography
• Exploring Curved Superspace
• Seiberg-Witten Theories on Ellipsoids
• The $\mathcal{N}=1$ Chiral Multiplet on $T^2\times S^2$ and Supersymmetric Localization
• Extended Supersymmetry on Curved Spaces
• The supersymmetric NUTs and bolts of holography
• Exploring Curved Superspace (II)
• Supersymmetry on curved spaces and superconformal anomalies
• Supercurrent anomalies in 4d SCFTs
• 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
• Rigid 4D N=2 supersymmetric backgrounds and actions
• Higher Derivative Supergravities in Diverse Dimensions
• Symmetries of curved superspace
• An introduction to supersymmetric field theories in curved space
• Supersymmetry anomalies in $\mathcal{N}=1$ conformal supergravity
• Symmetries of supergravity backgrounds and supersymmetric field theory
• N=2 SUSY gauge theories on S^4
• Killing superalgebras for Lorentzian four-manifolds
• Supersymmetric backgrounds from 5d N=1 supergravity
• Superconformal quantum field theory in curved spacetime
• Nonlinear sigma models with AdS supersymmetry in three dimensions
• Conformal symmetry superalgebras
• Semi-Chiral Operators in 4d $\mathcal{N}=1$ Gauge Theories
• Supersymmetry anomalies in new minimal supergravity
• Maximal super Yang-Mills theories on curved background with off-shell supercharges
• 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
• Supersymmetric Yang-Mills theory on conformal supergravity backgrounds in ten dimensions