Off-Shell ${\mathcal N}=(1,0)$ Linear Multiplets in Six Dimensions

TL;DR

This paper develops a tensor calculus for multiple ${ m N}=(1,0)$ linear multiplets in six dimensions, enabling new supersymmetric models and an off-diagonal superinvariant that yields $R^2$ supergravity.

Contribution

It introduces a tensor calculus for multiple linear multiplets and constructs new supersymmetric models, including an $R^2$ supergravity invariant.

Findings

Established a tensor calculus for ${ m N}=(1,0)$ linear multiplets

Constructed various supersymmetric models based on a function ${ m F}_{IJ}$

Derived an off-diagonal superinvariant leading to $R^2$ supergravity

Abstract

We provide a tensor calculus for $n$-number of ${\mathcal N}=(1,0)$ linear multiplets in six dimensions. The coupling of linear multiplets is encoded in a function ${\mathcal F}_{IJ}$ that is subject to certain constraints. We provide various rigid and local supersymmetric models depending on the choice of the function ${\mathcal F}_{IJ}$ and provide an interesting off-diagonal superinvariant, which leads to an $R^2$ supergravity upon elimination of auxiliary fields.