Supersymmetric domain walls in 7D maximal gauged supergravity

We give a large class of supersymmetric domain walls in maximal seven-dimensional gauged supergravity with various types of gauge groups. Gaugings are described by components of the embedding tensor transforming in representations $\mathbf{15}$ and $\overline{\mathbf{40}}$ of the global symmetry $SL(5)$. The embedding tensor in $\mathbf{15}$ representation leads to $CSO(p,q,5-p-q)$ gauge groups while gaugings in $\overline{\mathbf{40}}$ representation describes $CSO(p,q,4-p-q)$ gauge groups. These gaugings admit half-supersymmetric domain walls as vacuum solutions. On the other hand, gaugings involving both $\mathbf{15}$ and $\overline{\mathbf{40}}$ components lead to $\frac{1}{4}$-supersymmetric domain walls. In this case, the gauge groups under consideration are $SO(2,1)\ltimes \mathbf{R}^4$ and $CSO(2,0,2)\sim SO(2)\ltimes \mathbf{R}^4$. All of the domain wall solutions are analytically obtained. For $SO(5)$ gauge group, the gauged supergravity admits an $N=4$ supersymmetric $AdS_7$ vacuum dual to $N=(2,0)$ SCFT in six dimensions. The corresponding domain walls can be interpreted as holographic RG flows from the $N=(2,0)$ SCFT to non-conformal $N=(2,0)$ field theories in the IR. The solutions can be uplifted to eleven dimensions by using a truncation ansatz on $S^4$. Furthermore, the gauged supergravity with $CSO(4,0,1)\sim SO(4)\ltimes \mathbf{R}^4$ gauge group can be embedded in type IIA theory via a truncation on $S^3$. The uplifted domain walls, describing NS5-branes of type IIA theory, are also given.