Extended superconformal higher-spin gauge theories in four dimensions

TL;DR

This paper develops superconformal higher-spin gauge theories in four dimensions using off-shell ${ m extbf{N}}=2$ supergravity, constructing gauge-invariant actions and field strengths in curved backgrounds, including anti-de Sitter space.

Contribution

It introduces a new off-shell formulation for superconformal higher-spin multiplets and constructs gauge-invariant actions and field strengths in curved and AdS backgrounds.

Findings

Constructed superconformal higher-spin multiplets in curved backgrounds.

Developed gauge-invariant actions for these multiplets.

Presented field strengths forming representations of the ${ m extbf{N}}=2$ superconformal group.

Abstract

Using the off-shell formulation for ${\cal N}=2$ conformal supergravity in four dimensions, we describe superconformal higher-spin multiplets of conserved currents in a curved background and present their associated unconstrained gauge prepotentials. The latter are used to construct locally superconformal chiral actions, which are demonstrated to be gauge invariant in arbitrary conformally flat backgrounds. The main ${\cal N}=2$ results are then generalised to the ${\cal N}$-extended case. We also present the gauge-invariant field strengths for on-shell massless higher-spin ${\cal N}=2$ supermultiplets in anti-de Sitter space. These field strengths prove to furnish representations of the ${\cal N}=2$ superconformal group.