Supersymmetric domain walls in maximal 6D gauged supergravity III

We continue our study of gaugings the maximal $N=(2,2)$ supergravity in six dimensions with gauge groups obtained from decomposing the embedding tensor under ${\mathbb{R}}^{+}\times SO(4,4)$ subgroup of the global symmetry $SO(5,5)$. Supersymmetry requires the embedding tensor to transform in ${\mathbf{144}}_c$ representation of $SO(5,5)$. Under ${\mathbb{R}}^{+}\times SO(4,4)$ subgroup, this leads to the embedding tensor in $({\mathbf{8}}^{\pm 3}$, ${\mathbf{8}}^{\pm 1},{\mathbf{56}}^{\pm 1})$ representations. Gaugings in ${\mathbf{8}}^{\pm 3}$ representations lead to a translational gauge group ${\mathbb{R}}^8$ while gaugings in ${\mathbf{8}}^{\pm 1}$ representations give rise to gauge groups related to the scaling symmetry ${\mathbb{R}}^{+}$. On the other hand, the embedding tensor in ${\mathbf{56}}^{\pm 1}$ representations gives $CSO(4-p,p,1)\sim SO(4-p,p)⋉{\mathbb{R}}^4\subset SO(4,4)$ gauge groups with $p=0,1,2$. More interesting gauge groups can be obtained by turning on more than one representation of the embedding tensor subject to the quadratic constraints. In particular, we consider gaugings in both ${\mathbf{56}}^{-1}$ and ${\mathbf{8}}^{+3}$ representations giving rise to larger $SO(5-p,p)$ and $SO(4-p,p+1)$ gauge groups for $p=0,1,2$. In this case, we also give a number of half-supersymmetric domain wall solutions preserving different residual symmetries. The solutions for gaugings obtained only from ${\mathbf{56}}^{-1}$ representation are also included in these results when the ${\mathbf{8}}^{+3}$ part is accordingly turned off.