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Nonlinear sigma models with AdS supersymmetry in three dimensions
, 2012
"... In threedimensional antide Sitter (AdS) space, there exist several realizations of Nextended supersymmetry, which are traditionally labelled by two nonnegative integers p ≥ q such that p + q = N. Different choices of p and q, with N fixed, prove to lead to different restrictions on the target sp ..."
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Cited by 8 (6 self)
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In threedimensional antide Sitter (AdS) space, there exist several realizations of Nextended supersymmetry, which are traditionally labelled by two nonnegative integers p ≥ q such that p + q = N. Different choices of p and q, with N fixed, prove to lead to different restrictions on the target space geometry of supersymmetric nonlinear σmodels. We classify all possible types of hyperkähler target spaces for the cases N = 3 and N = 4 by making use of two different realizations for the most general (p, q) supersymmetric σmodels: (i) offshell formulations in terms of N = 3 and N = 4 projective supermultiplets; and (ii) onshell formulations in terms of covariantly chiral scalar superfields in (2,0) AdS superspace. Depending on the type of N = 3, 4 AdS supersymmetry, nonlinear σmodels can support one of the following target space geometries: (i) hyperkähler cones; (ii) noncompact hyperkähler manifolds with a U(1) isometry group which acts nontrivially on the twosphere of complex structures; (iii) arbitrary hyperkähler manifolds including compact ones. The option (iii) is realized only in the case of critical (4,0) AdS supersymmetry. As an application of the (4,0) AdS techniques developed, we also construct the most general nonlinear σmodel in Minkowski space with a noncentrally extended N = 4 Poincare ́ supersymmetry. Its target space is a hyperkähler cone (which is characteristic of N = 4 superconformal σmodels), but the σmodel is massive. The Lagrangian includes a positive potential constructed in terms of the homothetic conformal Killing vector the target space is endowed with. This mechanism of mass generation differs from the standard one which corresponds to a σmodel with the ordinary N = 4 Poincare ́ supersymmetry and which makes use of a triholomorphic Killing vector. ar
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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Cited by 6 (1 self)
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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