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 ${\alpha }^{\prime }$-corrected string theory compactified to six dimensions. Finally, we analyze the spectrum about the ${\text{AdS}}_3\times S^3$ solution.