Relating harmonic and projective descriptions of N=2 nonlinear sigma models

Recent papers have established the relationship between projective superspace and a complexified version of harmonic superspace. We extend this construction to the case of general nonlinear sigma models in both frameworks. Using an analogy with Hamiltonian mechanics, we demonstrate how the Hamiltonian structure of the harmonic action and the symplectic structure of the projective action naturally arise from a single unifying action on a complexified version of harmonic superspace. This links the harmonic and projective descriptions of hyperkahler target spaces. For the two examples of Taub-NUT and Eguchi-Hanson, we show how to derive the projective superspace solutions from the harmonic superspace solutions.Comment: 25 pages; v3: typo fixed in eq (1.36

Extended supersymmetric sigma models in AdS_4 from projective superspace

There exist two superspace approaches to describe N=2 supersymmetric nonlinear sigma models in four-dimensional anti-de Sitter (AdS_4) space: (i) in terms of N=1 AdS chiral superfields, as developed in arXiv:1105.3111 and arXiv:1108.5290; and (ii) in terms of N=2 polar supermultiplets using the AdS projective-superspace techniques developed in arXiv:0807.3368. The virtue of the approach (i) is that it makes manifest the geometric properties of the N=2 supersymmetric sigma-models in AdS_4. The target space must be a non-compact hyperkahler manifold endowed with a Killing vector field which generates an SO(2) group of rotations on the two-sphere of complex structures. The power of the approach (ii) is that it allows us, in principle, to generate hyperkahler metrics as well as to address the problem of deformations of such metrics. Here we show how to relate the formulation (ii) to (i) by integrating out an infinite number of N=1 AdS auxiliary superfields and performing a superfield duality transformation. We also develop a novel description of the most general N=2 supersymmetric nonlinear sigma-model in AdS_4 in terms of chiral superfields on three-dimensional N=2 flat superspace without central charge. This superspace naturally originates from a conformally flat realization for the four-dimensional N=2 AdS superspace that makes use of Poincare coordinates for AdS_4. This novel formulation allows us to uncover several interesting geometric results.Comment: 88 pages; v3: typos corrected, version published in JHE

Off-shell supergravity-matter couplings in three dimensions

We develop the superspace geometry of N-extended conformal supergravity in three space-time dimensions. General off-shell supergravity-matter couplings are constructed in the cases N=1,2,3,4.Comment: 73 pages; V5: typos in eqs. (3.4b), (3.17) and (4.24) correcte

Three-dimensional (p,q) AdS superspaces and matter couplings

We introduce N-extended (p,q) AdS superspaces in three space-time dimensions, with p+q=N and p>=q, and analyse their geometry. We show that all (p,q) AdS superspaces with X^{IJKL}=0 are conformally flat. Nonlinear sigma-models with (p,q) AdS supersymmetry exist for p+q4 the target space geometries are highly restricted). Here we concentrate on studying off-shell N=3 supersymmetric sigma-models in AdS_3. For each of the cases (3,0) and (2,1), we give three different realisations of the supersymmetric action. We show that (3,0) AdS supersymmetry requires the sigma-model to be superconformal, and hence the corresponding target space is a hyperkahler cone. In the case of (2,1) AdS supersymmetry, the sigma-model target space must be a non-compact hyperkahler manifold endowed with a Killing vector field which generates an SO(2) group of rotations of the two-sphere of complex structures.Comment: 52 pages; V3: minor corrections, version published in JHE

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

Six-dimensional Supergravity and Projective Superfields

We propose a superspace formulation of N=(1,0) conformal supergravity in six dimensions. The corresponding superspace constraints are invariant under super-Weyl transformations generated by a real scalar parameter. The known variant Weyl super-multiplet is recovered by coupling the geometry to a super-3-form tensor multiplet. Isotwistor variables are introduced and used to define projective superfields. We formulate a locally supersymmetric and super-Weyl invariant action principle in projective superspace. Some families of dynamical supergravity-matter systems are presented.Comment: 39 pages; v3: some modifications in section 2; equations (2.3), (2.14b), (2.16) and (2.17) correcte

Epidemic cerebrospinal meningitis in children at Federal Medical Centre, Gusau, Zamfara state, Nigeria

Epidemic meningococcal meningitis is a major public health problem still affecting tropical countries, particularly in Sub-Saharan Africa, which lieswithin African meningitis belt. Repeated large scale epidemics of CSM have been reported in northern Nigeria for the past four decades. It is one of the important causes of morbidity and mortality in these regions. Mortality from the CSM remains high despite advances in treatment modalities. Neisseria meningitidis serogroup A have been the major cause of large scale epidemics in tropical countries, while serogroups B, C, Y and W-135 are responsible for most of invasive disease in America and other developed countries.Objective: To determine the pattern of epidemic CSM in children atFederal Medical Centre, Gusau.Method: The study was a retrospective one carried out in children agedsix months to 12 years admitted into Emergency Paediatrics Unit (EPU) with a diagnosis of CSM within the period January to May, 2009.Results: Seventy- seven children with epidemic CSM were admittedand managed in EPU from January-May 2009.Conclusion: Neisseria meningitidis serogroup A CSM is becoming thedisease of young infants, and stresses the need for inclusion ofCSM vaccine in early infancy in routine immunization policy, in areas within the meningitis belt in Sub-Saharan Africa

N=2 supergravity and supercurrents

We address the problem of classifying all N=2 supercurrent multiplets in four space-time dimensions. For this purpose we consider the minimal formulation of N=2 Poincare supergravity with a tensor compensator, and derive its linearized action in terms of three N=2 off-shell multiplets: an unconstrained scalar superfield, a vector multiplet, and a tensor multiplet. Such an action was ruled out to exist in the past. Using the action constructed, one can derive other models for linearized N=2 supergravity by applying N=2 superfield duality transformations. The action depends parametrically on a constant non-vanishing real isotriplet g^{ij}=g^{ji} which originates as an expectation value of the tensor compensator. Upon reduction to N=1 superfields, we show that the model describes two dually equivalent formulations for the massless multiplet (1,3/2)+(3/2,2) depending on a choice of g^{ij}. In the case g^{11}=g^{22}=0, the action describes (i) new minimal N=1 supergravity; and (ii) the Fradkin-Vasiliev-de Wit-van Holten gravitino multiplet. In the case g^{12}=0, on the other hand, the action describes (i) old minimal N=1 supergravity; and (ii) the Ogievetsky-Sokatchev gravitino multiplet.Comment: 40 pages; v2: added references, some comments, new appendi

Superform formulation for vector-tensor multiplets in conformal supergravity

The recent papers arXiv:1110.0971 and arXiv:1201.5431 have provided a superfield description for vector-tensor multiplets and their Chern-Simons couplings in 4D N = 2 conformal supergravity. Here we develop a superform formulation for these theories. Furthermore an alternative means of gauging the central charge is given, making use of a deformed vector multiplet, which may be thought of as a variant vector-tensor multiplet. Its Chern-Simons couplings to additional vector multiplets are also constructed. This multiplet together with its Chern-Simons couplings are new results not considered by de Wit et al. in hep-th/9710212.Comment: 28 pages. V2: Typos corrected and references updated; V3: References updated and typo correcte

N=2 Conformal Superspace in Four Dimensions

We develop the geometry of four dimensional N=2 superspace where the entire conformal algebra of SU(2,2|2) is realized linearly in the structure group rather than just the SL(2,C) x U(2)_R subgroup of Lorentz and R-symmetries, extending to N=2 our prior result for N=1 superspace. This formulation explicitly lifts to superspace the existing methods of the N=2 superconformal tensor calculus; at the same time the geometry, when degauged to SL(2,C) x U(2)_R, reproduces the existing formulation of N=2 conformal supergravity constructed by Howe.Comment: 43 pages; v2 references added, acknowledgments update