Five-dimensional N=1N=1 AdS superspace: Geometry, off-shell multiplets and dynamics

As a step towards formulating projective superspace techniques for supergravity theories with eight supercharges, this work is devoted to field theory in five-dimensional N=1N=1 anti-de Sitter superspace AdS5|8=SU(2,2|1)/SO(4,1)×U(1)AdS5|8=SU(2,2|1)/SO(4,1)×U(1) which is a maximally symmetric curved background. We develop the differential geometry of AdS5|8AdS5|8 and describe its isometries in terms of Killing supervectors. Various off-shell supermultiplets in AdS5|8×S2AdS5|8×S2 are defined, and supersymmetric actions are constructed both in harmonic and projective superspace approaches. Several families of supersymmetric theories are presented including nonlinear sigma-models, Chern–Simons theories and vector–tensor dynamical systems. Using a suitable coset representative, we make use of the coset construction to develop an explicit realization for one half of the superspace AdS5|8AdS5|8 as a trivial fiber bundle with fibers isomorphic to four-dimensional Minkowski superspace.