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
and their conjugate superfields. Here we introduce CCL sigma models that are invariant under U(1) duality rotations exchanging the dynamical variables and their equations of motion. The Lagrangians of such sigma models prove to obey a partial differential equation that is analogous to the self-duality equation obeyed by U(1) duality invariant models for nonlinear electrodynamics. These sigma models are self-dual under a Legendre transformation that simultaneously dualises (i) the chiral multiplet into a complex linear one; and (ii) the complex linear multiplet into a chiral one. Any CCL sigma model possesses a dual formulation given in terms of two chiral multiplets. The U(1) duality invariance of the CCL sigma model proves to be equivalent, in the dual chiral formulation, to a manifest U(1) invariance rotating the two chiral scalars. Since the target space has a holomorphic Killing vector, the sigma model possesses a third formulation realised in terms of a chiral multiplet and a tensor multiplet. The family of U(1) duality invariant CCL sigma models includes a subset of N=2 supersymmetric theories. Their target spaces are hyper Kahler manifolds with a non-zero Killing vector field. In the case that the Killing vector field is triholomorphic, the sigma model admits a dual formulation in terms of a self-interacting off-shell N=2 tensor multiplet. We also identify a subset of CCL sigma models which are in a one-to-one correspondence with the U(1) duality invariant models for nonlinear electrodynamics. The target space isometry group for these sigma models contains a subgroup U(1) x U(1).
Free massless higher-superspin superfields on the N=1, D=4 anti-de Sitter superspace are introduced. The linearized gauge transformations are postulated. Two families of dually equivalent gauge-invariant action functionals are constructed for massles
s half-integer-superspin s+1/2 (s >= 2) and integer-superspin s (s >= 1) superfields. For s=1, one of the formulations for half-integer superspin multiplets reduces to linearized minimal N=1 supergravity with a cosmological term, while the other is the lifting to the anti-de Sitter superspace of linearized non-minimal n=-1 supergravity.
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
uperconformal sigma-model is superconformal. Since N = 2 superconformal sigma-models (for which target spaces are hyperkahler cones) formulated in terms of polar multiplets are naturally associated with Kahler cones (which are target spaces for N = 1 superconformal sigma-models), polar-polar duality generates a transformation between different Kahler cones. In the non-superconformal case, we study implications of polar-polar duality for the sigma-model formulation in terms of N = 1 chiral superfields. In particular, we find the relation between the original hyperkahler potential and its dual. As an application of polar-polar duality, we study self-dual models.
The superform construction of supergravity actions, christened the ectoplasm method, is based on the use of a closed super d-form in the case of d space-time dimensions. In known examples, such superforms are obtained by iteratively solving nontrivia
l cohomological problems. The latter usually makes this scheme no less laborious than the normal coordinate method for deriving component actions for matter-coupled supergravity. In this note we present an alternative procedure to generate required superforms in four space-time dimensions, which makes use of self-dual vector multiplets. It provides the shortest derivation of chiral actions in two different theories: (i) N = 1 old minimal supergravity; and (ii) N = 2 conformal supergravity. The N = 2 superform construction is developed here for the first time. Although our consideration is restricted to the case of four dimensions, a generalization to higher dimensions is plausible.
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)-dimen
sional 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.
The projective superspace formulation for four-dimensional N = 2 matter-coupled supergravity presented in arXiv:0805.4683 makes use of the variant superspace realization for the N = 2 Weyl multiplet in which the structure group is SL(2,C) x SU(2) and
the super-Weyl transformations are generated by a covariantly chiral parameter. An extension to Howes realization of N = 2 conformal supergravity in which the tangent space group is SL(2,C) x U(2) and the super-Weyl transformations are generated by a real unconstrained parameter was briefly sketched. Here we give the explicit details of the extension.
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 stru
cture 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.
Building on the five-dimensional constructions in hep-th/0601177, we provide a unified description of four-dimensional N = 2 superconformal off-shell multiplets in projective superspace, including a realization in terms of N = 1 superfields. In parti
cular, superconformal polar multiplets are consistently defined for the first time. We present new 4D N = 2 superconformal sigma-models described by polar multiplets. Such sigma-models realize general superconformal couplings in projective superspace, but involve an infinite tale of auxiliary N = 1 superfields. The auxiliaries should be eliminated by solving infinitely many algebraic nonlinear equations, and this is a nontrivial technical problem. We argue that the latter can be avoided by making use of supersymmetry considerations. All information about the resulting superconformal model (and hence the associated superconformal cone) is encoded in the so-called canonical coordinate system for a Kaehler metric, which was introduced by Bochner and Calabi in the late 1940s.
Starting with the projective-superspace off-shell formulation for four-dimensional N = 2 supersymmetric sigma-models on cotangent bundles of arbitrary Hermitian symmetric spaces, their on-shell description in terms of N = 1 chiral superfields is deve
loped. In particular, we derive a universal representation for the hyperkaehler potential in terms of the curvature of the symmetric base space. Within the tangent-bundle formulation for such sigma-models, completed recently in arXiv:0709.2633 and realized in terms of N = 1 chiral and complex linear superfields, we give a new universal formula for the superspace Lagrangian. A closed form expression is also derived for the Kaehler potential of an arbitrary Hermitian symmetric space in Kaehler normal coordinates.
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.
