Invariants for minimal conformal supergravity in six dimensions

TL;DR

This paper introduces a new off-shell formulation for six-dimensional conformal supergravity, constructs two key invariants with specific curvature terms, and proves their completeness in the minimal theory, also demonstrating a supersymmetric invariant construction.

Contribution

It develops a novel off-shell superspace formulation for 6D conformal supergravity and identifies all invariants of a certain type within this framework.

Findings

Constructed two invariants with $C^3$ and $Coxempty C$ terms.

Proved these are the only invariants in minimal conformal supergravity.

Demonstrated how to build the supersymmetric $F oxempty F$ invariant.

Abstract

We develop a new off-shell formulation for six-dimensional conformal supergravity obtained by gauging the 6D ${\cal N} = (1, 0)$ superconformal algebra in superspace. This formulation is employed to construct two invariants for 6D ${\cal N} = (1, 0)$ conformal supergravity, which contain $C^3$ and $C\Box C$ terms at the component level. Using a conformal supercurrent analysis, we prove that these exhaust all such invariants in minimal conformal supergravity. Finally, we show how to construct the supersymmetric $F \Box F$ invariant in curved superspace.