Conformally flat supergeometry in five dimensions

TL;DR

This paper develops the concept of conformally flat superspace in five dimensions using superspace formulation, enabling the formulation of various supersymmetric theories in terms of 4D N=1 superfields, with applications to anti-de Sitter space.

Contribution

It introduces a framework for conformally flat superspace in 5D, allowing supersymmetric theories to be expressed via 4D N=1 superfields, expanding the tools for higher-dimensional supergeometry.

Findings

Explicit procedure for formulating 5D supersymmetric theories in 4D superfields.

Application to anti-de Sitter superspace as an example.

Framework applicable to sigma-models and Yang-Mills theories.

Abstract

Using the superspace formulation for the 5D N = 1 Weyl supermultiplet developed in arXiv:0802.3953, we elaborate the concept of conformally flat superspace in five dimensions. For a large family of supersymmetric theories (including sigma-models and Yang-Mills theories) in the conformally flat superspace, we describe an explicit procedure to formulate their dynamics in terms of rigid 4D N = 1 superfields. The case of 5D N = 1 anti-de Sitter superspace is discussed as an example.