Gauss-Bonnet supergravity in six dimensions

The supersymmetrization of curvature squared terms is important in the study of the low-energy limit of compactified superstrings where a distinguished role is played by the Gauss-Bonnet combination, which is ghost-free. In this letter, we construct its off-shell $\mathcal{N}=(1,0)$ supersymmetrization in six dimensions for the first time. By studying this invariant together with the supersymmetric Einstein-Hilbert term we confirm and extend known results of the ${\alpha }^{\mathrm{\prime }}$-corrected string theory compactified to six dimensions. Finally, we analyze the spectrum about the ${\mathrm{A}\mathrm{d}\mathrm{S}}_3\times {\mathrm{S}}^3$ solution.