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arXiv · 1404.2636

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

Cyril Closset·Stefano Cremonesi
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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 $Ω$-background on the sphere. We also systematically work out the curved-space supersymmetry multiplets and supersymmetric Lagrangians.

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Cyril Closset, Stefano Cremonesi. 2014-07-01. Comments on N=(2,2) Supersymmetry on Two-Manifolds. https://doi.org/10.1007/jhep07(2014)075

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