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

Closset, Cyril; Cremonesi, Stefano

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Cyril Closset


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.


Closset, C., & Cremonesi, S. (2014). Comments on N = (2, 2) supersymmetry on two-manifolds. Journal of High Energy Physics, 2014(07), Article 075.

Journal Article Type Article
Acceptance Date Jun 27, 2014
Online Publication Date Jul 16, 2014
Publication Date Jul 16, 2014
Deposit Date Feb 2, 2017
Publicly Available Date Mar 29, 2017
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2014
Issue 07
Article Number 075
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Published Journal Article (911 Kb)

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Copyright 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.

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