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

TL;DR

The paper develops covariant, off-shell formalisms for five-dimensional ${ m N}=1$ AdS superspace ${ m AdS}^{5|8}$ by constructing its covariant derivative algebra and isometries, then implementing harmonic and projective superspace techniques on ${ m AdS}^{5|8} imes S^2$ to formulate a broad class of supersymmetric actions. It provides explicit analytic and projective multiplets, action principles, and dynamical systems (including nonlinear sigma-models, vector multiplets, Chern-Simons, and tensor multiplets) within these frameworks, and culminates with a coset-space realization that connects the AdS geometry to a four-dimensional Minkowski-like subspace. The results offer a covariant toolkit for eight-supercharge supergravity contexts and lay groundwork for future explorations of AdS superspace dynamics and holographic applications.

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) x 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} x 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 isomorophic to four-dimensional Minkowski superspace.