Abstract
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 = 1 anti-de Sitter superspace AdS 5 | 8 = SU ( 2 , 2 | 1 ) / SO ( 4 , 1 ) × U ( 1 ) which is a maximally symmetric curved background. We develop the differential geometry of AdS 5 | 8 and describe its isometries in terms of Killing supervectors. Various off-shell supermultiplets in AdS 5 | 8 × S 2 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 AdS 5 | 8 as a trivial fiber bundle with fibers isomorphic to four-dimensional Minkowski superspace.
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