49,972 research outputs found
New extended superconformal sigma models and Quaternion Kahler manifolds
Quaternion Kahler manifolds are known to be the target spaces for matter
hypermultiplets coupled to N=2 supergravity. It is also known that there is a
one-to-one correspondence between 4n-dimensional quaternion Kahler manifolds
and those 4(n+1)-dimensional hyperkahler spaces which are the target spaces for
rigid superconformal hypermultiplets (such spaces are called hyperkahler
cones). In this paper we present a projective-superspace construction to
generate a hyperkahler cone M^{4(n+1)}_H of dimension 4(n+1) from a
2n-dimensional real analytic Kahler-Hodge manifold M^{2n}_K. The latter emerges
as a maximal Kahler submanifold of the 4n-dimensional quaternion Kahler space
M^{4n}_Q such that its Swann bundle coincides with M^{4(n+1)}_H. Our approach
should be useful for the explicit construction of new quaternion Kahler
metrics. The results obtained are also of interest, e.g., in the context of
supergravity reduction N=2 --> N=1, or alternatively from the point of view of
embedding N=1 matter-coupled supergravity into an N=2 theory.Comment: 30 page
N = 2 supersymmetric sigma-models and duality
For two families of four-dimensional off-shell N = 2 supersymmetric nonlinear
sigma-models constructed originally in projective superspace, we develop their
formulation in terms of N = 1 chiral superfields. Specifically, these theories
are: (i) sigma-models on cotangent bundles T*M of arbitrary real analytic
Kaehler manifolds M; (ii) general superconformal sigma-models described by
weight-one polar supermultiplets. Using superspace techniques, we obtain a
universal expression for the holomorphic symplectic two-form \omega^{(2,0)}
which determines the second supersymmetry transformation and is associated with
the two complex structures of the hyperkaehler space T*M that are complimentary
to the one induced from M. This two-form is shown to coincide with the
canonical holomorphic symplectic structure. In the case (ii), we demonstrate
that \omega^{(2,0)} and the homothetic conformal Killing vector determine the
explicit form of the superconformal transformations. At the heart of our
construction is the duality (generalized Legendre transform) between off-shell
N = 2 supersymmetric nonlinear sigma-models and their on-shell N = 1 chiral
realizations. We finally present the most general N = 2 superconformal
nonlinear sigma-model formulated in terms of N = 1 chiral superfields. The
approach developed can naturally be generalized in order to describe 5D and 6D
superconformal nonlinear sigma-models in 4D N = 1 superspace.Comment: 31 pages, no figures; V2: reference and comments added, typos
corrected; V3: more typos corrected, published versio
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