Comments on N=(2,2) Supersymmetry on Two-Manifolds

Abstract

We study curved-space rigid supersymmetry for two-dimensional $\mathcal{N}=(2,2)$ supersymmetric fields theories with a vector-like $R$-symmetry by coupling such theories to background supergravity. The associated Killing spinors can be viewed as holomorphic sections of particular complex line bundles over Euclidean space-time, which severely restrict the allowed supersymmetric couplings on compact orientable Riemann surfaces without boundaries. For genus $g>1$, the only consistent non-singular couplings are the ones dictated by the topological $A$-twist. On spaces with $S^2$ topology, there exist additional supersymmetric backgrounds with $m=0$ or $\pm 1$ unit of flux for the $R$-symmetry gauge field. The $m=-1$ case includes the $\Omega$-background on the sphere. We also systematically work out the curved-space supersymmetry multiplets and supersymmetric Lagrangians.

38 pages+appendix; v2: new section 6.10 on NLSM Lagrangians; v3: corrected typos and added references

References in corpus (3)

• Sphere Partition Functions and the Zamolodchikov Metric
• New N = (2, 2) vector multiplets
• Nonabelian Generalized Gauge Multiplets

Cited by in corpus (11)

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• Ω-deformation and quantization
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• Ω-deformation of B-twisted gauge theories and the 3d-3d correspondence
• A-twisted correlators and Hori dualities
• Janus interface entropy and Calabi's diastasis in four-dimensional $\mathcal{N}=2$ superconformal field theories
• Recent developments in 2d $\mathcal{N}=(2,2)$ supersymmetric gauge theories
• Gauge and matter superfield theories on $S^2$
• Localization of Gauged Linear Sigma Model for KK5-branes
• The coupling of Poisson sigma models to topological backgrounds