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Symmetries of curved superspace
 JHEP
, 2013
"... The formalism to determine (conformal) isometries of a given curved superspace was elaborated almost two decades ago in the context of the old minimal formulation for N = 1 supergravity in four dimensions (4D). This formalism is universal, for it may readily be generalized to supersymmetric backgro ..."
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The formalism to determine (conformal) isometries of a given curved superspace was elaborated almost two decades ago in the context of the old minimal formulation for N = 1 supergravity in four dimensions (4D). This formalism is universal, for it may readily be generalized to supersymmetric backgrounds associated with any supergravity theory formulated in superspace. In particular, it has already been used to construct rigid supersymmetric field theories in 5D N = 1, 4D N = 2 and 3D (p, q) antide Sitter superspaces. In the last two years, there have appeared a number of publications devoted to the construction of supersymmetric backgrounds in offshell 4D N = 1 supergravity theories using component field considerations. Here we demonstrate how to read off the key results of these recent publications from the more general superspace approach developed in the 1990s. We also present a universal superspace setting to construct supersymmetric backgrounds, which is applicable to any of the known offshell formulations for N = 1 supergravity. This approach is based on the realizations of the new minimal and nonminimal supergravity theories as superWeyl invariant couplings of the old minimal supergravity to certain conformal compensators. ar
Revised version: March, 2014 N = 4 supersymmetric YangMills theories in AdS3
, 2014
"... For all types of N = 4 antide Sitter (AdS) supersymmetry in three dimensions, we construct manifestly supersymmetric actions for Abelian vector multiplets and explain how to extend the construction to the nonAbelian case. Manifestly N = 4 supersymmetric YangMills (SYM) actions are explicitly give ..."
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For all types of N = 4 antide Sitter (AdS) supersymmetry in three dimensions, we construct manifestly supersymmetric actions for Abelian vector multiplets and explain how to extend the construction to the nonAbelian case. Manifestly N = 4 supersymmetric YangMills (SYM) actions are explicitly given in the cases of (2,2) and critical (4,0) AdS supersymmetries. The N = 4 vector multiplets and the corresponding actions are then reduced to (2,0) AdS superspace, in which only N = 2 supersymmetry is manifest. Using the offshell structure of the N = 4 vector multiplets, we provide complete N = 4 SYM actions in (2,0) AdS superspace for all types of N = 4 AdS supersymmetry. In the case of (4,0) AdS supersymmetry, which admits a Euclidean counterpart, the resulting N = 2 action contains a ChernSimons term proportional to q/r, where r is the radius of AdS3 and q is the Rcharge of a chiral scalar superfield. The Rcharge is a linear inhomogeneous function of X, an expectation value of the N = 4 Cotton superfield. Thus our results explain the mysterious structure of N = 4 supersymmetric YangMills theories on S3 discovered in arXiv:1401.7952. In the case of (3,1) AdS supersymmetry, which has no Euclidean counterpart, the SYM action contains both a ChernSimons term and a chiral masslike term. In the case of (2,2) AdS supersymmetry, which admits a Euclidean counterpart, the SYM action has no ChernSimons and chiral masslike terms.ar X iv