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

## TL;DR

This paper develops the geometry and superspace techniques for five-dimensional N=1 anti-de Sitter superspace, constructing off-shell multiplets and supersymmetric actions, advancing supergravity formulations with eight supercharges.

## Contribution

It introduces the differential geometry of AdS^{5|8}, defines off-shell supermultiplets, and constructs supersymmetric actions using harmonic and projective superspace methods.

## Key findings

- Developed the geometry and isometries of AdS^{5|8}
- Constructed various off-shell supermultiplets and actions
- Presented new supersymmetric theories including sigma-models and Chern-Simons

## 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.