Supersymmetric domain walls in maximal 6D gauged supergravity III

Abstract

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 $CSO(4-p,p,1)\sim SO(4-p,p)\ltimes \mathbb{R}^4\subset SO(4,4)$ 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.