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Nonlinear sigma models with AdS supersymmetry in three dimensions
, 2012
"... In three-dimensional anti-de Sitter (AdS) space, there exist several realizations of N-extended supersymmetry, which are traditionally labelled by two non-negative 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 three-dimensional anti-de Sitter (AdS) space, there exist several realizations of N-extended supersymmetry, which are traditionally labelled by two non-negative 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 σ-models. 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 σ-models: (i) off-shell formulations in terms of N = 3 and N = 4 projective supermultiplets; and (ii) on-shell formulations in terms of covariantly chiral scalar superfields in (2,0) AdS superspace. Depending on the type of N = 3, 4 AdS supersymmetry, nonlinear σ-models can support one of the following target space geometries: (i) hyperkähler cones; (ii) non-compact hyperkähler manifolds with a U(1) isometry group which acts non-trivially on the two-sphere 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 σ-model in Minkowski space with a non-centrally extended N = 4 Poincare ́ supersymmetry. Its target space is a hyperkähler cone (which is characteristic of N = 4 superconformal σ-models), but the σ-model 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 σ-model with the ordinary N = 4 Poincare ́ supersymmetry and which makes use of a tri-holomorphic 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 formula-tion 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 formula-tion 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) anti-de Sitter superspaces. In the last two years, there have appeared a number of publications devoted to the construction of supersymmetric backgrounds in off-shell 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 off-shell formulations for N = 1 supergravity. This approach is based on the realizations of the new minimal and non-minimal super-gravity theories as super-Weyl invariant couplings of the old minimal supergravity to certain conformal compensators. ar
