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Comments on N = (2, 2) supersymmetry on two-manifolds.

Closset, Cyril and Cremonesi, Stefano (2014) 'Comments on N = (2, 2) supersymmetry on two-manifolds.', Journal of high energy physics., 2014 (07). 075.


We study curved-space rigid supersymmetry for two-dimensional NN = (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 restricts 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 S2 topology, there exist additional supersymmetric backgrounds with m = 0 or ±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.

Item Type:Article
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Publisher statement:Open Access, © The Author(s) 2014. Article funded by SCOAP3. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Date accepted:27 June 2014
Date deposited:29 March 2017
Date of first online publication:16 July 2014
Date first made open access:No date available

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