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

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.