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Register a new userThree-dimensional N=2 supergravity theories: From superspace to components
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Gabriele Tartaglino-Mazzucchelli
Publication date
2013
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English
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For general off-shell N=2 supergravity-matter systems in three spacetime dimensions, a formalism is developed to reduce the corresponding actions from superspace to components. The component actions are explicitly computed in the cases of Type I and Type II minimal supergravity formulations. We describe the models for topologically massive supergravity which correspond to all the known off-shell formulations for three-dimensional N=2 supergravity. We also present a universal setting to construct supersymmetric backgrounds associated with these off-shell supergravities.
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This paper presents a projective superspace formulation for 4D N = 2 matter-coupled supergravity. We first describe a variant superspace realization for the N = 2 Weyl multiplet. It differs from that proposed by Howe in 1982 by the choice of the structure group (SO(3,1) x SU(2) versus SO(3,1) x U(2)), which implies that the super-Weyl transformations are generated by a covariantly chiral parameter instead of a real unconstrained one. We introduce various off-shell supermultiplets which are curved superspace analogues of the superconformal projective multiplets in global supersymmetry and which describe matter fields coupled to supergravity. A manifestly locally supersymmetric and super-Weyl invariant action principle is given. Off-shell locally supersymmetric nonlinear sigma models are presented in this new superspace.
The superspace formulation for four-dimensional N = 2 matter-coupled supergravity recently developed in arXiv:0805.4683 makes use of a new type of conformal compensator with infinitely many off-shell degrees of freedom: the so-called covariant weight-one polar hypermultiplet. In the present note we prove the duality of this formulation to the known minimal (40+40) off-shell realization for N = 2 Poincare supergravity involving the improved tensor compensator. Within the latter formulation, we present new off-shell matter couplings realized in terms of covariant weight-zero polar hypermultiplets. We also elaborate upon the projective superspace description of vector multiplets in N = 2 conformal supergravity. An alternative superspace representation for locally supersymmetric chiral actions is given. We present a model for massive improved tensor multiplet with both ``electric and ``magnetic types. of mass terms.
The superspace formulation of N=1 conformal supergravity in four dimensions is demonstrated to be equivalent to the conventional component field approach based on the superconformal tensor calculus. The detailed correspondence between two approaches is explicitly given for various quantities; superconformal gauge fields, curvatures and curvature constraints, general conformal multiplets and their transformation laws, and so on. In particular, we carefully analyze the curvature constraints leading to the superconformal algebra and also the superconformal gauge fixing leading to Poincare supergravity since they look rather different between two approaches.
We obtain cosmological solutions with Kasner-like asymptotics in N=2 gauged and ungauged supergravity by maximal analytic continuation of plan
We give a classification of fully supersymmetric chiral ${cal N}=(8,0)$ AdS$_3$ vacua in general three-dimensional half-maximal gauged supergravities coupled to matter. These theories exhibit a wealth of supersymmetric vacua with background isometries given by the supergroups OSp$(8|2,mathbb{R})$, F(4), SU$(4|1,1)$, and OSp$(4^*|4)$, respectively. We identify the associated embedding tensors and the structure of the associated gauge groups. We furthermore compute the mass spectra around these vacua. As an off-spin we include results for a number of ${cal N}=(7,0)$ vacua with supergroups OSp$(7|2,mathbb{R})$ and G$(3)$, respectively. We also comment on their possible higher-dimensional uplifts.
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