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This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)kahler reduction; projective superspace; the generalized Legendre construction; generalized Kahler geometry and constructions of hyperkahler metrics on Hermitean symmetric spaces.
We study dualities in off-shell 4D N = 2 supersymmetric sigma-models, using the projective superspace approach. These include (i) duality between the real O(2n) and polar multiplets; and (ii) polar-polar duality. We demonstrate that the dual of any s
We continue our study of a general class of $mathcal{N}=2$ supersymmetric $AdS_3times Y_7$ and $AdS_2times Y_9$ solutions of type IIB and $D=11$ supergravity, respectively. The geometry of the internal spaces is part of a general family of GK geometr
Supersymmetric non-linear sigma-models are described by a field dependent Kaehler metric determining the kinetic terms. In general it is not guaranteed that this metric is always invertible. Our aim is to investigate the symmetry structure of supersy
In four-dimensional N=1 Minkowski superspace, general nonlinear sigma models with four-dimensional target spaces may be realised in term of CCL (chiral and complex linear) dynamical variables which consist of a chiral scalar, a complex linear scalar
It is known that supersymmetric nonlinear sigma models for the compact Kahler manifolds G/H cannot be consistently coupled to supergravity, since the Kahler potentials are not invariant under the G transformation. We show that the supersymmetric nonl